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

%I A356655 #14 Aug 21 2022 06:13:03
%S A356655 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,
%T A356655 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,
%U A356655 399,1,435,1,3,1,465465,1,3,1,255,1,483,1,15,1,33,1
%N A356655 Clausen numbers based on the strictly proper divisors of n, 1 < d < n.
%F A356655 a(n) = Product_{d | n} (d + 1), where d + 1 is prime and 1 < d < n.
%p A356655 clausen := proc(n) numtheory[divisors](n) minus {1, n};
%p A356655 map(i -> i+1, %); select(isprime, %); mul(i, i=%)  end:
%p A356655 seq(clausen(n), n = 0..80);
%t A356655 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 *)
%o A356655 (PARI) a(n) = if (n, vecprod(select(isprime, apply(x->x+1, setminus(divisors(n), [1,n])))), 1); \\ _Michel Marcus_, Aug 21 2022
%Y A356655 Cf. A160014, A166120.
%K A356655 nonn
%O A356655 0,5
%A A356655 _Peter Luschny_, Aug 20 2022