A278914 a(n) is the smallest odd number k with prime sum of divisors such that tau(k) = n-th prime.

9, 2401, 729, 9765625, 531441, 45949729863572161, 5559917313492231481, 1471383076677527699142172838322885948765175969, 10264895304762966931257013446474591264089923314972889033759201, 230466617897195215045509519405933293401

Offset

2,1

Comments

tau(n) = A000005(n) = the number of divisors of n.

For n >= 7; a(n) > A023194(10000) = 5896704025969.

Links

Robert G. Wilson v, Table of n, a(n) for n = 2..66 (first 49 terms from Davin Park)

Formula

a(n) = A101636(n)^(prime(n)-1). - Davin Park, Dec 10 2016

Example

a(2) = 9 because 9 is the smallest odd number with prime values of sum of divisors (sigma(9) = 13) such that tau(9) = 3 = 2nd prime.

Mathematica

A278914[n_] := NestWhile[NextPrime, 3, ! PrimeQ[Cyclotomic[Prime[n], #]] &]^(Prime[n] - 1); Array[A278914, 10, 2] (* Davin Park, Dec 28 2016 *)

Prog

(Magma) A278914:=func<n|exists(r){k:k in[1..10000000] | IsOdd(k) and IsPrime(SumOfDivisors(k)) and NumberOfDivisors(k) eq NthPrime(n)} select r else 0>; [A278914(n): n in[2..6]]
(PARI) a(n) = {my(k=1); while(! (isprime(sigma(k)) && isprime(p=numdiv(k)) && (primepi(p) == n)), k+=2); k; } \\ Michel Marcus, Dec 03 2016

Crossrefs

Cf. A000005, A000203, A278911, A278913.

Sequence in context: A013827 A058428 A323517 * A069704 A033997 A068729

Adjacent sequences: A278911 A278912 A278913 * A278915 A278916 A278917

Keyword

nonn,more

Author

Jaroslav Krizek, Nov 30 2016

Extensions

More terms from Davin Park, Dec 11 2016

Status

approved