A353382 Inverse Möbius transform of A353380.

1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 1, 1, 1, 5, 2, 2, 3, 4, 1, 3, 1, 4, 2, 1, 2, 7, 1, 2, 1, 4, 1, 3, 1, 3, 4, 1, 1, 6, 2, 3, 2, 4, 1, 5, 1, 5, 1, 2, 1, 7, 1, 1, 3, 5, 2, 3, 1, 3, 2, 3, 1, 9, 1, 2, 4, 4, 2, 3, 1, 4, 3, 1, 1, 7, 1, 2, 1, 4, 1, 7, 1, 3, 2, 1, 2, 8, 1, 4, 4, 6, 1, 3, 1, 5, 3

Offset: 1

Author

Antti Karttunen, Apr 19 2022

Keywords

• nonn

Comments

Number of terms of A353355 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, A048675, A332823, A348717, A353352, A353354, A353355, A353380, A353381.

Programs

PARI

A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
A353354(n) = sumdiv(n,d,A332823(d));
A353380(n) = (0==A353354(n));
A353382(n) = sumdiv(n,d,A353380(d));

Formula

a(n) = Sum_{d|n} A353380(d).

a(n) = A000005(n) - A353381(n).

a(p) = 1 for all primes p.

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