OFFSET
1,8
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 27 2023
STATUS
approved