A324810 Sum of A324828(d) over the divisors d of n.

0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 4, 1, 2, 2, 2, 1, 4, 1, 4, 3, 2, 1, 4, 2, 2, 2, 4, 1, 4, 1, 2, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 4, 4, 2, 1, 4, 2, 5, 2, 4, 1, 4, 3, 4, 2, 2, 1, 6, 1, 2, 4, 2, 2, 4, 1, 4, 2, 4, 1, 6, 1, 2, 4, 4, 2, 4, 1, 4, 2, 2, 1, 8, 2, 2, 2, 4, 1, 8, 3, 4, 2, 2, 2, 4, 1, 3, 4, 6, 1, 4, 1, 4, 4

Offset: 1

Author

Antti Karttunen, Mar 17 2019

Keywords

• nonn

Comments

Inverse Möbius transform of A324828.

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. A000203, A156552, A323243, A324543, A324712, A324823, A324825, A324828.

Programs

PARI

A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.
A324828(n) = (A324712(n)%2);
A324810(n) = sumdiv(n,d,A324828(d));

Formula

a(n) = Sum_{d|n} A324828(d).

a(p) = 1 for all primes p.

A000035(a(n)) = A324823(n) = A323243(n) mod 2.