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

Author

Jaroslav Krizek, Nov 30 2016

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A000203, A023194, A278914.

Programs

Magma

A278913:=func; [A278913(n): n in[1..8]];

Mathematica

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

PARI

a(n) = {my(k=1); while(! (isprime(sigma(k)) && isprime(p=numdiv(k)) && (primepi(p) == n)), k++); k;} \\ Michel Marcus, Dec 03 2016

Formula

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

Extensions

More terms from Davin Park, Dec 08 2016