A324575 a(1) = 0; for n > 1, a(n) = A033879(A048675(n)).

0, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 5, 0, 1, 1, 4, 1, 0, 2, 16, 1, 4, 1, 18, 0, 2, 1, 6, 1, 4, -3, 46, -4, 0, 1, 82, 14, 6, 1, 10, 1, -3, 1, 256, 1, 0, 1, 5, -12, 14, 1, 6, -2, 10, 8, 226, 1, 1, 1, 748, -4, 0, -19, 18, 1, -12, -12, 12, 1, 6, 1, 1362, 2, 8, -12, 22, 1, 1, 1, 3838, 1, -4, 10, 5458, 254, 18, 1, 5, -10, -12, -348, 12250

Offset: 1

Author

Antti Karttunen, Mar 07 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• 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. A007947, A033879, A048675, A324573, A324574.

Cf. also A323244, A323174, A324546.

Programs

PARI

A033879(n) = (2*n-sigma(n));
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A324575(n) = if(1==n,0,A033879(A048675(n)));

Formula

a(1) = 0; for n > 1, a(n) = A033879(A048675(n)).

a(n) = 2*A048675(n) - A324573(n).

a(A007947(n)) = A324574(n).

a(p) = 1 for all primes p.