A366904 The sum of exponentially evil divisors of n.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A004709, A366902, A366906.

Similar sequences: A353900, A365682, A366903.

Sequence in context: A264981 A370240 A113061 * A284099 A176410 A087966

Adjacent sequences: A366901 A366902 A366903 * A366905 A366906 A366907

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 27 2023

Status

approved