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%I #10 May 04 2024 04:49:28
%S 1,2,2,0,2,4,2,4,0,4,2,0,2,4,4,0,2,0,2,0,4,4,2,8,0,4,4,0,2,8,2,0,4,4,
%T 4,0,2,4,4,8,2,8,2,0,0,4,2,0,0,0,4,0,2,8,4,8,4,4,2,0,2,4,0,0,4,8,2,0,
%U 4,8,2,0,2,4,0,0,4,8,2,0,0,4,2,0,4,4,4
%N Multiplicative with a(p^e) = e+1 if e+1 is a power of 2, and 0 otherwise.
%H Amiram Eldar, <a href="/A372470/b372470.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A359473(n)*A000005(n).
%F a(A036537(n)) = A000005(A036537(n)) = A372468(n).
%t f[p_, e_] := If[e + 1 == 2^IntegerExponent[e + 1, 2], e + 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = vecprod(apply(x -> if(x+1 == 1 << valuation(x+1, 2), x+1, 0), factor(n)[, 2]));
%Y Cf. A000005, A036537, A359473, A372468.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, May 02 2024
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