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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 (list; graph; refs; listen; history; text; internal format)
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: A093178 A307153 A336898 * A328478 A093411 A147088

Adjacent sequences:  A300327 A300328 A300329 * A300331 A300332 A300333

KEYWORD

nonn

AUTHOR

Peter Luschny, Mar 12 2018

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)