A193267 The number 1 alternating with the numbers A006953/A002445 (which are integers).

1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 16, 1, 18, 1, 20, 1, 2, 1, 24, 1, 2, 1, 4, 1, 6, 1, 32, 1, 2, 1, 36, 1, 2, 1, 40, 1, 42, 1, 4, 1, 2, 1, 48, 1, 2, 1, 4, 1, 54, 1, 8, 1, 2, 1, 60, 1, 2, 1, 64, 1, 6, 1, 4, 1, 2, 1, 72, 1, 2, 1, 4, 1, 6, 1, 80, 1, 2, 1, 84, 1, 2, 1, 8, 1, 18, 1, 4, 1, 2, 1, 96, 1, 2, 1, 100

Offset

1,2

Comments

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 divides n. - Peter Luschny, Mar 12 2018

Links

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

Formula

a(n+1) = A185633(n+1)/A027760(n+1).

a(n+1) = c(n+2)/c(n+1).

Maple

with(numtheory); a := proc(n) divisors(n); map(i->i+1, %); select(isprime, %);
mul(k^padic[ordp](n, k), k=%) end: seq(a(n), n=1..100); # Peter Luschny, Mar 12 2018
# Alternatively:
A193267 := 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 divides(f[1]-1, n) then
P := P*f[1]^f[2] fi od; P end: seq(A193267(n), n=1..100); # Peter Luschny, Mar 12 2018

Mathematica

a[n_] := If[OddQ[n], 1, Denominator[ BernoulliB[n]/n ] / Denominator[ BernoulliB[n]] ]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 21 2012 *)

Prog

(Magma) [Denominator(Bernoulli(n)/n)/Denominator(Bernoulli(n)): n in [1..100]]; // Vincenzo Librandi, Mar 12 2018
(Julia)
using Nemo
function A193267(n) P = 1
    for (p, e) in factor(ZZ(n))
        divisible(ZZ(n), p - 1) && (P *= p^e) end
P end
[A193267(n) for n in 1:100] |> println # Peter Luschny, Mar 12 2018

Crossrefs

Sequence in context: A329379 A328479 A340346 * A327832 A083258 A083259

Adjacent sequences: A193264 A193265 A193266 * A193268 A193269 A193270

Keyword

nonn

Author

Paul Curtz, Dec 20 2012

Status

approved