OFFSET
1,4
FORMULA
a(n) = Product_{d|n} d^((1+d') mod 2), where d' is the arithmetic derivative of d.
EXAMPLE
a(8) = 32; the product of the divisors of 8 whose arithmetic derivative is even is 4*8 = 32.
MATHEMATICA
d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := Product[k^Mod[d[k] + 1, 2], {k, Divisors[n]}]; Array[a, 60] (* Amiram Eldar, May 13 2022 *)
PROG
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = vecprod(select(x->!(ad(x) % 2), divisors(n))); \\ Michel Marcus, May 13 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 12 2022
STATUS
approved