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

1,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A193267, A195989, A300711.

Sequence in context: A307153 A339421 A336898 * A328478 A093411 A147088

Adjacent sequences: A300327 A300328 A300329 * A300331 A300332 A300333

Keyword

nonn

Author

Peter Luschny, Mar 12 2018

Status

approved