A353381 Number of divisors of n not in A353355.

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

Offset: 1

Author

Antti Karttunen, Apr 19 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, A048675, A332823, A348717, A353352, A353354, A353355, A353380, A353382.

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));
A353381(n) = sumdiv(n,d,!A353380(d));

Formula

a(n) = Sum_{d|n} 1-A353380(d).

a(n) = A000005(n) - A353382(n).

a(p) = 1 for all primes p.

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