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%I #7 Oct 28 2023 03:47:30
%S 1,1,1,1,1,1,1,9,1,1,1,1,1,1,1,9,1,1,1,1,1,1,1,9,1,1,28,1,1,1,1,41,1,
%T 1,1,1,1,1,1,9,1,1,1,1,1,1,1,9,1,1,1,1,1,28,1,9,1,1,1,1,1,1,1,105,1,1,
%U 1,1,1,1,1,9,1,1,1,1,1,1,1,9,28,1,1,1,1
%N The sum of exponentially evil divisors of n.
%C The number of these divisors is A366902(n) and the largest of them is A366906(n).
%H Amiram Eldar, <a href="/A366904/b366904.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = 1 + Sum_{k = 1..e, k is evil} p^k.
%F a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
%t f[p_, e_] := 1 + Total[p^Select[Range[e], EvenQ[DigitCount[#, 2, 1]] &]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(k = 1, f[i, 2], !(hammingweight(k)%2) * f[i, 1]^k));}
%Y Cf. A004709, A366902, A366906.
%Y Similar sequences: A353900, A365682, A366903.
%K nonn,easy,mult
%O 1,8
%A _Amiram Eldar_, Oct 27 2023
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