A278913 a(n) is the smallest number k with prime sum of divisors such that tau(k) = n-th prime.

2, 4, 16, 64, 9765625, 4096, 65536, 262144, 1471383076677527699142172838322885948765175969, 10264895304762966931257013446474591264089923314972889033759201, 1073741824, 18701397461209715023927088008788055619800417991632621566284510161

Offset

1,1

Comments

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.

Links

Davin Park, Table of n, a(n) for n = 1..50

Formula

a(n) = A123487(n)^(prime(n)-1). - Davin Park, Dec 10 2016

Example

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.

Mathematica

A278913[n_] := NestWhile[NextPrime, 2, ! PrimeQ[Cyclotomic[Prime[n], #]] &]^(Prime[n] - 1) (* Davin Park, Dec 28 2016 *)

Prog

(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

Crossrefs

Cf. A000005, A000203, A023194, A278914.

Sequence in context: A288756 A019279 A061652 * A306979 A358032 A162119

Adjacent sequences: A278910 A278911 A278912 * A278914 A278915 A278916

Keyword

nonn

Author

Jaroslav Krizek, Nov 30 2016

Extensions

More terms from Davin Park, Dec 08 2016

Status

approved