A051464 - OEIS

%I #13 Sep 16 2021 02:26:12

%S 2,2,2,2,4,4,2,2,4,2,4,2,4,6,4,4,16,2,4,2,4,2,4,8,12,8,2,4,8,4,4,4,4,

%T 4,4,8,8,4,8,16,8,4,8,8,6,16,8,8,8,16,8,4,32,32,8,4,8,4,4,8,16,8,8,16,

%U 48,16,16,8,4,16,4,16,16,8,8,8,16,16,8,16,32

%N Number of divisors of 4*(2^n-1) + 1.

%C Create a table with tau(2^n-1) as the first row (A046801) and tau(m) as the first column (A000005). The second column is tau(A004760) and so on. Rows 2, 3 and 4 are easily described in terms of row 1. This sequence is row 5.

%H Sean A. Irvine, <a href="/A051464/b051464.txt">Table of n, a(n) for n = 1..591</a>

%F a(n) = tau(4*(2^n -1)+1), where d(n) = A000005(n).

%t Array[DivisorSigma[0, 4*(2^# - 1) + 1] &, 81] (* _Michael De Vlieger_, Sep 15 2021 *)

%o (PARI) a(n) = numdiv(4*(2^n-1) + 1); \\ _Michel Marcus_, Sep 16 2021

%Y Cf. A000005, A036563.

%K nonn

%O 1,1

%A Edwin D. Evans, eevans2(AT)pacbell.net

%E a(81) corrected by _Sean A. Irvine_, Sep 15 2021