A336695 a(n) = A331410(1+sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.

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

Offset: 1

Author

Antti Karttunen, Jul 31 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A088580, A324294, A331410, A332459, A336691, A336692, A336693, A336694, A336696.

Programs

PARI

A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
A336695(n) = A331410(1+sigma(n));

Formula

a(n) = A331410(1+A000203(n)) = A331410(A088580(n)) = A331410(A332459(n)).