A353371 Number of divisors of n that are not in A325698.

0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 4, 1, 2, 2, 4, 1, 4, 1, 5, 3, 3, 1, 6, 2, 2, 3, 4, 1, 5, 1, 5, 2, 3, 2, 6, 1, 2, 3, 7, 1, 5, 1, 5, 4, 3, 1, 8, 2, 5, 2, 4, 1, 6, 3, 6, 3, 2, 1, 9, 1, 3, 5, 6, 2, 5, 1, 5, 2, 5, 1, 9, 1, 2, 4, 4, 2, 5, 1, 9, 4, 3, 1, 8, 3, 2, 3, 7, 1, 8, 3, 5, 2, 3, 2, 10, 1, 4, 4, 8, 1, 5, 1, 6, 5

Offset: 1

Author

Antti Karttunen, Apr 16 2022

Keywords

• nonn

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, A348717, A353370, A353372.

Programs

PARI

A353370(n) = { my(f = factor(n)); (0==sum(i=1, #f~, f[i,2]*((-1)^(primepi(f[i, 1])%2)))); };
A353371(n) = sumdiv(n,d,!A353370(d));

Formula

a(n) = Sum_{d|n} 1-A353370(d).

a(n) = A000005(n) - A353372(n).

a(p) = 1 for all primes p.

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