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

Author

Jaroslav Krizek, Nov 30 2016

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A000203, A278911, A278913.

Programs

Magma

A278914:=func; [A278914(n): n in[2..6]];

Mathematica

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

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

Formula

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

Extensions

More terms from Davin Park, Dec 11 2016