A324865 a(n) = A323243(n) - A156552(n).

0, 0, 1, 1, 3, 1, 7, 1, 6, 4, 15, 1, 31, 1, 8, 9, 63, 1, 127, 1, 21, 15, 255, 1, 16, 19, 10, 13, 511, 11, 1023, 1, 20, 47, 22, 13, 2047, 1, 78, 17, 4095, 1, 8191, 1, 14, 287, 16383, 1, 36, 6, 122, 1, 32767, 1, 55, 1, 270, 277, 65535, 1, 131071, 687, 22, 41, 58, 27, 262143, 45, 260, 1, 524287, 17, 1048575, 259, 16

Offset: 1

Author

Antti Karttunen, Mar 18 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• 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. A001065, A156552, A323243, A324866, A324867, A324868.

Programs

PARI

A001065(n) = (sigma(n)-n);
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A324865(n) = if(1==n,0,A001065(A156552(n)));

PARI

A324865(n) = (A323243(n) - A156552(n)); \\ Needs also code from A323243.

Formula

a(1) = 0; for n > 1, a(n) = A001065(A156552(n)).

a(n) = A323243(n) - A156552(n).