A353975 Product of the divisors of n whose arithmetic derivative is odd.

1, 2, 3, 2, 5, 36, 7, 2, 3, 100, 11, 36, 13, 196, 15, 2, 17, 648, 19, 100, 21, 484, 23, 36, 5, 676, 81, 196, 29, 54000, 31, 2, 33, 1156, 35, 648, 37, 1444, 39, 100, 41, 148176, 43, 484, 675, 2116, 47, 36, 7, 5000, 51, 676, 53, 944784, 55, 196, 57, 3364, 59, 54000, 61, 3844

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = Product_{d|n} d^((d') mod 2), where d' is the arithmetic derivative of d.

Example

a(6) = 36; the product of the divisors of 6 whose arithmetic derivative is odd is 2*3*6 = 36.

Mathematica

d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := Product[k^Mod[d[k], 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

Cf. A003415 (n'), A353976.

Sequence in context: A085307 A361581 A361580 * A078599 A183103 A183105

Adjacent sequences: A353972 A353973 A353974 * A353976 A353977 A353978

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2022

Status

approved