A072341 - OEIS

%I #9 Nov 07 2017 18:30:31

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A072341/b072341.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A034693(A000203(n)). - _Antti Karttunen_, Nov 07 2017

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

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

%o (PARI) A072341(n) = { my(k=1,s=sigma(n)); while(!isprime(1+(k*s)),k++); k; }; \\ _Antti Karttunen_, Nov 07 2017

%Y Cf. A000203, A034693, A034694, A072344.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Jul 16 2002