login
A193267
The number 1 alternating with the numbers A006953/A002445 (which are integers).
5
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
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
KEYWORD
nonn
AUTHOR
Paul Curtz, Dec 20 2012
STATUS
approved