%I #11 Feb 18 2022 08:06:14

%S 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,

%T 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,

%U 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

%N 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).

%H Antti Karttunen, <a href="/A351555/b351555.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o 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)); };

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

%K nonn

%O 1,29

%A _Antti Karttunen_, Feb 16 2022