A324573 a(1) = 0; for n > 1, a(n) = sigma(A048675(n)).

0, 1, 3, 3, 7, 4, 15, 4, 7, 6, 31, 7, 63, 13, 12, 7, 127, 6, 255, 12, 18, 18, 511, 6, 15, 48, 12, 18, 1023, 8, 2047, 6, 39, 84, 28, 12, 4095, 176, 54, 8, 8191, 12, 16383, 39, 15, 258, 32767, 12, 31, 13, 144, 54, 65535, 8, 42, 12, 252, 800, 131071, 15, 262143, 1302, 28, 12, 91, 20, 524287, 144, 528, 14, 1048575, 8, 2097151, 2736, 18

Offset: 1

Author

Antti Karttunen, Mar 08 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's prime signature data)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A048675, A324574, A324575.

Cf. also A277892, A322812, A323243.

Programs

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A324573(n) = if(1==n,0,sigma(A048675(n)));

Formula

a(1) = 0; for n > 1, a(n) = A000203(A048675(n)).