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A366904
The sum of exponentially evil divisors of n.
6
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, 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, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 28, 1, 1, 1, 1
OFFSET
1,8
COMMENTS
The number of these divisors is A366902(n) and the largest of them is A366906(n).
LINKS
FORMULA
Multiplicative with a(p^e) = 1 + Sum_{k = 1..e, k is evil} p^k.
a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
MATHEMATICA
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]
PROG
(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)); }
CROSSREFS
Similar sequences: A353900, A365682, A366903.
Sequence in context: A264981 A370240 A113061 * A284099 A176410 A087966
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 27 2023
STATUS
approved