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A278913
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a(n) is the smallest number k with prime sum of divisors such that tau(k) = n-th prime.
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2
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2, 4, 16, 64, 9765625, 4096, 65536, 262144, 1471383076677527699142172838322885948765175969, 10264895304762966931257013446474591264089923314972889033759201, 1073741824, 18701397461209715023927088008788055619800417991632621566284510161
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OFFSET
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1,1
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COMMENTS
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tau(n) = A000005(n) = the number of divisors of n.
a(11) = 1073741824; a(n) > A023194(10000) = 5896704025969 for n = 9, 10 and n >= 12.
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 16 because 16 is the smallest number with prime values of sum of divisors (sigma(16) = 31) such that tau(16) = 5 = 3rd prime.
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MATHEMATICA
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A278913[n_] := NestWhile[NextPrime, 2, ! PrimeQ[Cyclotomic[Prime[n], #]] &]^(Prime[n] - 1) (* Davin Park, Dec 28 2016 *)
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PROG
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(Magma) A278913:=func<n|exists(r){k:k in[1..10000000] | IsPrime(SumOfDivisors(k)) and NumberOfDivisors(k) eq NthPrime(n)} select r else 0>; [A278913(n): n in[1..8]]
(PARI) a(n) = {my(k=1); while(! (isprime(sigma(k)) && isprime(p=numdiv(k)) && (primepi(p) == n)), k++); k; } \\ Michel Marcus, Dec 03 2016
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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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