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A353975
Product of the divisors of n whose arithmetic derivative is odd.
1
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 12 2022
STATUS
approved