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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.
2
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Mar 12 2018
STATUS
approved