Search: a344859 -id:a344859
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A344897
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a(n) is the number of divisors of 10^n + 1.
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+10
13
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2, 2, 2, 8, 4, 4, 4, 4, 4, 32, 8, 24, 8, 8, 16, 128, 32, 16, 8, 4, 16, 192, 16, 32, 8, 32, 8, 128, 16, 8, 128, 4, 16, 384, 16, 32, 64, 16, 8, 768, 16, 8, 128, 16, 16, 4096, 16, 16, 512, 16, 128, 256, 16, 4, 64, 768, 32, 64, 32, 16, 64, 8, 8, 3072, 8, 64, 256, 4, 16, 1024, 2048, 8, 32, 16, 128, 2048, 64, 3072, 128, 16
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OFFSET
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0,1
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COMMENTS
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a(n) is even because 10^n + 1 is not a square number.
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LINKS
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FORMULA
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MATHEMATICA
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a[0] = 2; a[n_] := DivisorSigma[0, 10^n + 1]; Array[a, 60, 0] (* Amiram Eldar, Jun 01 2021 *)
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PROG
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(PARI) a(n) = numdiv(10^n+1);
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CROSSREFS
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Cf. A000005, A000533, A003021, A038371, A046798, A057934, A070528, A119704, A344859, A087021, A087022,
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A334167
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a(n) is the number of divisors of n^n-1.
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+10
6
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2, 4, 8, 12, 16, 16, 96, 128, 48, 16, 256, 48, 32, 128, 128, 40, 512, 12, 2048, 768, 256, 64, 6144, 4096, 768, 512, 4096, 768, 24576, 16, 6144, 768, 8192, 1024, 262144, 1152, 256, 1024, 49152, 256, 65536, 64, 24576, 196608, 384, 32, 393216, 327680, 12288, 24576
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OFFSET
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2,1
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COMMENTS
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25 values of the first 40 are powers of 2.
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := DivisorSigma[0, n^n - 1]; a /@ Range[2, 45] (* Giovanni Resta, Apr 17 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A344869
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Number of distinct prime factors of n^n+1.
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+10
3
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1, 1, 1, 2, 1, 3, 3, 3, 3, 4, 3, 6, 4, 5, 5, 6, 2, 3, 7, 5, 3, 6, 4, 8, 6, 7, 5, 11, 6, 7, 10, 7, 4, 11, 6, 13, 5, 7, 7, 8, 9, 6, 10, 8, 8, 14, 8, 10, 6, 7, 10, 11, 5, 8, 14, 11, 7, 13, 13, 9, 12, 8, 7, 18, 4, 12, 8, 7, 7, 16, 9, 8, 12, 4, 8, 24, 7, 9, 14, 7, 5, 12, 6, 12, 8, 13, 10, 12, 10, 6, 23, 15, 6, 9, 11, 16, 3, 8, 17, 23, 7
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OFFSET
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0,4
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LINKS
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FORMULA
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MATHEMATICA
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a[0] = 1; a[n_] := PrimeNu[n^n + 1]; Array[a, 45, 0] (* Amiram Eldar, May 31 2021 *)
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PROG
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(PARI) a(n) = omega(n^n+1);
(Magma) [#PrimeDivisors(n^n+1): n in [0..100]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A366820
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a(n) is the sum of the divisors of n^n + 1.
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+10
1
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3, 3, 6, 56, 258, 6264, 52136, 1559520, 17041416, 706911048, 10102223208, 706019328000, 9101898907920, 519285252355776, 11672709747324912, 880565163670372352, 18446811354131136516, 1792353900753729655758, 54357680125881245248800, 4154723599066412190910560
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) a(n) = sigma(n^n+1);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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