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%I #12 Dec 23 2018 16:13:15
%S 0,1,2,1,2,2,2,1,2,2,2,2,2,3,1,1,2,2,2,2,2,2,2,2,2,4,2,3,2,2,2,1,2,2,
%T 2,2,2,4,1,2,2,2,2,2,1,3,2,2,2,2,2,4,2,2,1,3,2,2,2,2,2,4,2,1,3,1,2,2,
%U 2,2,2,2,2,4,1,4,3,3,2,2,2,2,2,2,2,6,1,2,2,2,2,3,2,3,2,2,2,3,2,2,2,2,2,4,4
%N Number of odd divisors of Sopf(n).
%C Sopf(n) is the sum of the distinct primes dividing n (A008472).
%H Antti Karttunen, <a href="/A193523/b193523.txt">Table of n, a(n) for n = 1..20000</a>
%F a(1) = 0; for n > 1, a(n) = A001227(A008472(n)). - _Antti Karttunen_, Dec 23 2018
%e a(26) = 4 because Sopf(26) = 15 and the 4 odd divisors are {1, 3, 5, 15}.
%t f[n_] := Block[{d=Divisors[Plus@@First[Transpose[FactorInteger[n]]]]}, Count[OddQ[d],True]]; Table[f[n], {n,100}]
%o (PARI)
%o A001227(n) = numdiv(n>>valuation(n, 2));
%o A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472
%o A193523(n) = if(1==n,0,A001227(A008472(n))); \\ _Antti Karttunen_, Dec 23 2018
%Y Cf. A001227, A008472.
%K nonn
%O 1,3
%A _Michel Lagneau_, Jul 29 2011
%E More terms from _Antti Karttunen_, Dec 23 2018
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