A072341 a(n) = the least natural number k such that k*sigma(n) + 1 is prime.

1, 2, 1, 4, 1, 1, 2, 2, 4, 1, 1, 1, 2, 3, 3, 10, 1, 2, 2, 1, 3, 1, 3, 1, 10, 1, 1, 2, 1, 1, 3, 2, 2, 2, 2, 6, 5, 1, 2, 2, 1, 1, 2, 4, 1, 1, 2, 3, 4, 4, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 5, 1, 3, 4, 4, 3, 2, 1, 1, 3, 1, 6, 2, 2, 3, 2, 1, 2, 3, 2, 6, 1, 4, 2, 1, 3, 2, 1, 2, 4, 1, 2, 2, 3, 2, 3, 2, 12, 1, 6, 1, 2, 3

Offset: 1

Author

Joseph L. Pe, Jul 16 2002

Keywords

• nonn

Comments

Conjecture: a(n) is less than or equal to n for all n.

Examples

			sigma(4) = 7 and the least natural number k such that 7 k + 1 is prime is k = 4; so a(4) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000203, A034693, A034694, A072344.

Programs

Mathematica

f[n_] := Module[{i}, i = 0; While[ ! PrimeQ[i*DivisorSigma[1, n] + 1], i++ ]; i]; Table[f[i], {i, 1, 150}]

PARI

A072341(n) = { my(k=1,s=sigma(n)); while(!isprime(1+(k*s)),k++); k; }; \\ Antti Karttunen, Nov 07 2017

Formula

a(n) = A034693(A000203(n)). - Antti Karttunen, Nov 07 2017