OFFSET
1,3
LINKS
FORMULA
a(n) = A000026(n) if n odd, a(n) = a(n/2) if n even.
From Amiram Eldar, Nov 12 2022: (Start)
Multiplicative with a(2^e) = 1 and a(p^e) = e*p for p > 2.
Sum_{k=1..n} a(k) ~ c * n^2, where c = (6*zeta(2)^2/17) * Product_{p prime} (1 - 3/p^2 + 2/p^3 + 1/p^4 - 1/p^5) = 0.2947570019... . (End)
EXAMPLE
a(54) = a(2 * 3^3) = 3 * 3 = 9.
MAPLE
a:= n-> mul(`if`(i[1]=2, 1, i[1]*i[2]), i=ifactors(n)[2]):
seq(a(n), n=1..75); # Alois P. Heinz, Feb 03 2021
MATHEMATICA
a[n_] := Times @@ (#[[1]] #[[2]] & /@ FactorInteger[n/2^IntegerExponent[n, 2]]); Table[a[n], {n, 75}]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 1]==2, 1, f[i, 1] * f[i, 2])); } \\ Amiram Eldar, Nov 12 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Feb 03 2021
STATUS
approved