A336315 The number of divisors in the conjugated prime factorization of n: a(n) = A000005(A122111(n)).

1, 2, 3, 2, 4, 4, 5, 2, 3, 6, 6, 4, 7, 8, 6, 2, 8, 4, 9, 6, 9, 10, 10, 4, 4, 12, 3, 8, 11, 8, 12, 2, 12, 14, 8, 4, 13, 16, 15, 6, 14, 12, 15, 10, 6, 18, 16, 4, 5, 6, 18, 12, 17, 4, 12, 8, 21, 20, 18, 8, 19, 22, 9, 2, 16, 16, 20, 14, 24, 12, 21, 4, 22, 24, 6, 16, 10, 20, 23, 6, 3, 26, 24, 12, 20, 28, 27, 10, 25, 8, 15, 18, 30, 30, 24

Offset: 1

Author

Antti Karttunen, Jul 18 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65539
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A034444, A122111, A286621, A323173, A322813, A322819, A336316.

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));

Formula

a(n) = A000005(A122111(n)).

a(n) = A336316(n) + A034444(n).