A356655 Clausen numbers based on the strictly proper divisors of n, 1 < d < n.

1, 1, 1, 1, 3, 1, 3, 1, 15, 1, 3, 1, 105, 1, 3, 1, 15, 1, 21, 1, 165, 1, 3, 1, 1365, 1, 3, 1, 15, 1, 231, 1, 255, 1, 3, 1, 25935, 1, 3, 1, 165, 1, 21, 1, 345, 1, 3, 1, 23205, 1, 33, 1, 15, 1, 399, 1, 435, 1, 3, 1, 465465, 1, 3, 1, 255, 1, 483, 1, 15, 1, 33, 1

Offset: 0

Author

Peter Luschny, Aug 20 2022

Keywords

• nonn

Crossrefs

Cf. A160014, A166120.

Programs

Maple

clausen := proc(n) numtheory[divisors](n) minus {1, n};
map(i -> i+1, %); select(isprime, %); mul(i, i=%)  end:
seq(clausen(n), n = 0..80);

Mathematica

a[n_] := Product[If[1 < d < n && PrimeQ[d + 1], d + 1, 1], {d, Divisors[n]}]; Array[a, 100, 0] (* Amiram Eldar, Aug 20 2022 *)

PARI

a(n) = if (n, vecprod(select(isprime, apply(x->x+1, setminus(divisors(n), [1,n])))), 1); \\ Michel Marcus, Aug 21 2022

Formula

a(n) = Product_{d | n} (d + 1), where d + 1 is prime and 1 < d < n.