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%I #16 Jul 06 2022 06:57:29
%S 0,1,0,1,0,0,0,1,0,0,0,0,0,0,3,1,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,1,2,0,
%T 4,0,0,0,4,0,0,4,0,0,3,0,0,0,0,0,4,0,0,0,4,0,2,0,0,2,0,0,2,1,3,4,0,0,
%U 2,2,0,0,0,0,3,0,3,3,0,0,0,0,0,4,2,0
%N Number of even divisors of sopf(n).
%C Sopf(n) is the sum of the distinct primes dividing n (A008472).
%H Charles R Greathouse IV, <a href="/A193525/b193525.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A183063(A008472(n)). - _Amiram Eldar_, Jul 06 2022
%e a(15) = 3 because sopf(15) = 8 and its 3 even divisors are {2, 4, 8}.
%t f[n_] := Block[{d=Divisors[Plus@@First[Transpose[FactorInteger[n]]]]}, Count[EvenQ[d],True]]; Table[f[n] ,{n,100}]
%t Array[Count[Divisors[Total[FactorInteger[#][[All,1]]]],_?EvenQ]&,100] (* _Harvey P. Dale_, Jun 20 2019 *)
%t even[n_] := (e = IntegerExponent[n, 2]) * DivisorSigma[0, n / 2^e]; a[n_] := even[Plus @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* _Amiram Eldar_, Jul 06 2022 *)
%o (PARI) sopf(n:int)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
%o a(n)=if(n==1,0,n=sopf(n);if(n%2,0,numdiv(n/2))) \\ _Charles R Greathouse IV_, Jul 31 2011
%Y Cf. A008472, A183063.
%K nonn
%O 1,15
%A _Michel Lagneau_, Jul 29 2011
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