A072056 - OEIS

%I #14 Apr 26 2024 05:58:21

%S 2,2,2,4,2,4,4,4,2,2,6,6,2,4,4,2,4,4,8,4,6,4,2,2,8,4,6,4,4,2,8,2,6,6,

%T 4,4,12,4,4,2,2,6,2,6,4,8,6,4,8,8,2,2,8,2,4,4,6,4,8,2,10,2,8,4,8,4,8,

%U 12,4,4,4,2,12,6,8,4,4,8,4,12,2,4,2,6,4,2,4,8,4,6,8,4,12

%N Number of divisors of 2*prime(n)+1.

%H Amiram Eldar, <a href="/A072056/b072056.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(A072055(n)).

%e Divisors of A072055(8) = 2*A000040(8)+1 = 2*19+1=39: {1,3,13,39} with size 4, therefore a(8) = 4.

%t Table[DivisorSigma[0,2Prime[n]+1],{n,100}] (* _Harvey P. Dale_, Apr 12 2021 *)

%o (PARI) a(n) = numdiv(2*prime(n)+1); \\ _Amiram Eldar_, Apr 26 2024

%o (PARI) lista(pmax) = forprime(p = 2, pmax, print1(numdiv(2*p+1), ", ")); \\ _Amiram Eldar_, Apr 26 2024

%Y Cf. A000005, A000040, A072055, A072057.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 11 2002