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The sum of exponentially evil divisors of n.
6

%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