A323905 a(n) = A156552(n) - A048675(n).

0, 0, 0, 1, 0, 2, 0, 4, 2, 4, 0, 7, 0, 8, 4, 11, 0, 8, 0, 13, 8, 16, 0, 18, 4, 32, 8, 25, 0, 14, 0, 26, 16, 64, 8, 21, 0, 128, 32, 32, 0, 26, 0, 49, 14, 256, 0, 41, 8, 16, 64, 97, 0, 22, 16, 60, 128, 512, 0, 35, 0, 1024, 26, 57, 32, 50, 0, 193, 256, 28, 0, 48, 0, 2048, 16, 385, 16, 98, 0, 71, 22, 4096, 0, 63, 64, 8192, 512, 116, 0, 36, 32, 769, 1024

Offset: 1

Author

Antti Karttunen, Feb 12 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A048675, A156552, A323906 (rgs-transform).

Programs

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ From A048675
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A323905(n) = (A156552(n) - A048675(n));

Formula

a(n) = A156552(n) - A048675(n).