Search: a248052 -id:a248052
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A248054
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Least positive integer m such that m + n divides sigma(m^2) + sigma(n^2), where sigma(k) is the sum of all positive divisors of k.
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+10
4
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1, 3, 2, 7, 24, 34, 3, 81, 209, 16, 63, 25, 7, 20, 140, 10, 3, 10, 22, 2, 39, 4, 35, 5, 4, 2, 28, 27, 75, 41, 16, 78, 44, 6, 23, 14, 207, 59, 21, 84, 17, 78, 7, 3, 11725, 10, 5, 2, 1669, 361, 134, 10, 141, 310, 21, 73, 21, 33, 38, 121
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) exists for any n > 0.
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LINKS
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EXAMPLE
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a(4) = 7 since 7 + 4 = 11 divides sigma(7^2) + sigma(4^2) = 57 + 31 = 88.
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MATHEMATICA
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Do[m=1; Label[aa]; If[Mod[DivisorSigma[1, m^2]+DivisorSigma[1, n^2], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
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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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A248354
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Least positive integer m such that m + n divides prime(m^2) + prime(n^2).
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+10
1
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1, 1, 2, 1, 3, 8, 2, 6, 6, 45, 9, 4, 15, 2, 13, 17, 4, 12, 9, 8, 11, 6, 101, 20, 2, 15, 7, 50, 4, 183, 48, 15, 9, 5, 4, 4, 157, 1, 123, 4, 13, 112, 76, 4, 7, 13, 44, 2, 16, 28, 83, 202, 114, 50, 85, 31, 14, 62, 19, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1)/2 for all n > 1.
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LINKS
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EXAMPLE
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a(3) = 2 since 2 + 3 = 5 divides prime(2^2) + prime(3^2) = 7 + 23 = 30.
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MATHEMATICA
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Do[m = 1; Label[aa]; If[Mod[Prime[m^2] + Prime[n^2], m + n] == 0, Print[n, " ", m]; Goto[bb]]; m = m + 1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
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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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STATUS
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approved
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