A353372 Inverse Möbius transform of A353370.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 4, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 3, 1, 2, 3

Offset: 1

Author

Antti Karttunen, Apr 16 2022

Keywords

• nonn

Comments

Number of terms of A325698 that divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A003961, A325698, A353370, A353371.

Programs

PARI

A353370(n) = { my(f = factor(n)); (0==sum(i=1, #f~, f[i,2]*((-1)^(primepi(f[i, 1])%2)))); };
A353372(n) = sumdiv(n,d,A353370(d));

Formula

a(n) = Sum_{d|n} A353370(d).

a(n) = A000005(n) - A353371(n).

a(p) = 1 for all primes p.

a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.