A300330 a(n) is the product over all prime powers p^e where p^e is the highest power of p dividing n and p-1 does not divide n.

1, 1, 3, 1, 5, 1, 7, 1, 9, 5, 11, 1, 13, 7, 15, 1, 17, 1, 19, 1, 21, 11, 23, 1, 25, 13, 27, 7, 29, 5, 31, 1, 33, 17, 35, 1, 37, 19, 39, 1, 41, 1, 43, 11, 45, 23, 47, 1, 49, 25, 51, 13, 53, 1, 55, 7, 57, 29, 59, 1, 61, 31, 63, 1, 65, 11, 67, 17, 69, 35, 71, 1

Offset: 1

Author

Peter Luschny, Mar 12 2018

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A193267, A195989, A300711.

Programs

Julia

using Nemo
function A300330(n) P = 1
    for (p, e) in factor(ZZ(n))
        ! divisible(ZZ(n), p - 1) && (P *= p^e) end
P end
[A300330(n) for n in 1:72] |> println

Magma

[n/(Denominator(Bernoulli(n)/n)/Denominator(Bernoulli(n))): n in [1..100]]; // Vincenzo Librandi, Mar 12 2018

Maple

A300330 := proc(n) local P, F, f, divides; divides := (a,b) -> is(irem(b,a) = 0):
P := 1; F := ifactors(n)[2]; for f in F do if not divides(f[1]-1, n) then
P := P*f[1]^f[2] fi od; P end: seq(A300330(n), n=1..100);

Mathematica

a[n_]:=If[OddQ[n], 1, Denominator[BernoulliB[n]/n]/Denominator[BernoulliB[n]]]; Table[n/a[n], {n, 1, 100}] (* Vincenzo Librandi, Mar 12 2018 *)

Formula

a(n) * A193267(n) = n.