A336928 a(n) = A329697(sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.

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

Offset: 1

Author

Antti Karttunen, Aug 11 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, A329697.

Cf. also A336469, A336694, A336927, A336929.

Programs

PARI

A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A336928(n) = A329697(sigma(n));

Formula

Additive with a(p^e) = A329697(sigma(p^e)) = A329697(1+ p + p^2 + ... + p^e).

a(n) = A329697(A000203(n)).