A351555 a(n) is the number of odd prime factors of sigma(n) that do not divide A003961(n) and the valuation(n, p) is different from valuation(sigma(n), p).

0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0

Offset: 1

Author

Antti Karttunen, Feb 16 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
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A351551, A351554 (positions of zeros), A351553 (even terms there), A351543.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351555(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); sum(k=1,#f~,if((f[k,1]%2) && 0!=(u%f[k,1]), (valuation(n,f[k,1])!=f[k,2]), 0)); };