cp's OEIS Frontend

A353332 Number of divisors d of n for which both A001222(d) and A056239(d) are even.

%I A353332 #12 Apr 15 2022 10:33:26
%S A353332 1,1,1,2,1,1,1,2,2,2,1,2,1,1,1,3,1,2,1,3,2,2,1,2,2,1,2,2,1,2,1,3,1,2,
%T A353332 1,4,1,1,2,4,1,2,1,3,2,2,1,3,2,3,1,2,1,2,2,2,2,1,1,3,1,2,3,4,1,2,1,3,
%U A353332 1,2,1,4,1,1,2,2,1,2,1,5,3,2,1,4,2,1,2,4,1,4,2,3,1,2,1,3,1,2,2,5,1,2,1,2,2
%N A353332 Number of divisors d of n for which both A001222(d) and A056239(d) are even.
%C A353332 Number of terms of A340784 that divide n.
%H A353332 Antti Karttunen, <a href="/A353332/b353332.txt">Table of n, a(n) for n = 1..65537</a>
%H A353332 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353332 a(n) = Sum_{d|n} A353331(d).
%F A353332 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%e A353332 Of the 9 divisors of 36, only divisors 1, 4, 9 and 36 satisfy the condition, therefore a(36) = 4.
%o A353332 (PARI)
%o A353332 A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
%o A353332 A353331(n) = ((!(bigomega(n)%2)) && (!(A056239(n)%2)));
%o A353332 A353332(n) = sumdiv(n,d,A353331(d));
%Y A353332 Cf. A001222, A003961, A056239, A340784, A348717.
%Y A353332 Inverse Möbius transform of A353331. Cf. also A353333, A353334.
%Y A353332 Differs from A353362 for the first time at n=30, where a(30) = 2, while A353362(30) = 3.
%K A353332 nonn
%O A353332 1,4
%A A353332 _Antti Karttunen_, Apr 14 2022