A336316 The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).

0, 0, 1, 0, 2, 0, 3, 0, 1, 2, 4, 0, 5, 4, 2, 0, 6, 0, 7, 2, 5, 6, 8, 0, 2, 8, 1, 4, 9, 0, 10, 0, 8, 10, 4, 0, 11, 12, 11, 2, 12, 4, 13, 6, 2, 14, 14, 0, 3, 2, 14, 8, 15, 0, 8, 4, 17, 16, 16, 0, 17, 18, 5, 0, 12, 8, 18, 10, 20, 4, 19, 0, 20, 20, 2, 12, 6, 12, 21, 2, 1, 22, 22, 4, 16, 24, 23, 6, 23, 0, 11, 14, 26, 26, 20, 0, 24

Offset: 1

Author

Antti Karttunen, Jul 18 2020

Keywords

• nonn

Comments

Equally, the number of divisors in the conjugated prime factorization of n minus the number of its unitary divisors.

Note that A001221(A122111(n)) = A001221(n) for all n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A001221, A034444, A048105, A122111, A286621, A336315.

Cf. A055932 (the positions of zeros).

Programs

PARI

A336315(n) = if(1==n,n,my(p=apply(primepi,factor(n)[,1]~),m=1+p[1]); for(i=2, #p, m *= (1+p[i]-p[i-1])); (m));
A336316(n) = (A336315(n)-(2^omega(n)));

Formula

a(n) = A336315(n) - A034444(n) = A000005(A122111(n)) - 2^A001221(n).

a(n) = A048105(A122111(n)).