A334455 - OEIS

%I #40 Nov 12 2020 01:16:36

%S 1,2,3,5,7,4,5,4,6,13,5,8,17,6,9,19,10,10,7,11,11,8,8,12,12,13,9,9,7,

%T 6,15,31,8,16,11,17,12,18,18,19,13,13,13,8,10,10,11,11,22,9,12,24,10,

%U 25,17,17,13,13,14,14,14,19,12,12,15,15,61,21,16,32,13

%N a(n) is unique integer k such that sigma(A051281(n)) = tau(A051281(n))^k (where sigma is the sum of divisors (A000203) and tau the number of divisors (A000005)), with a(1) = 1.

%H Rémy Sigrist, <a href="/A334455/b334455.txt">Table of n, a(n) for n = 1..12885</a>

%H Rémy Sigrist, <a href="/A334455/a334455.png">Colored scatterplot of the first 12885 terms</a> (where the color is function of tau(A051281(n)))

%H Rémy Sigrist, <a href="/A334455/a334455.gp.txt">PARI program for A334455</a>

%F a(n) = log(A000203(A051281(n))) / log(A000005(A051281(n))) for n > 1.

%e For n = 7:

%e - A051281(7) = 889,

%e - sigma(889) = 1024,

%e - tau(889) = 4,

%e - 1024 = 4^5,

%e - so a(7) = 5.

%o (PARI) See Links section.

%Y Cf. A000005, A000203, A051281, A225369.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Nov 10 2020