cp's OEIS Frontend

A363520 Product of the divisors of n that are < sqrt(n).

%I A363520 #20 Jun 17 2023 11:21:35
%S A363520 1,1,1,1,1,2,1,2,1,2,1,6,1,2,3,2,1,6,1,8,3,2,1,24,1,2,3,8,1,30,1,8,3,
%T A363520 2,5,24,1,2,3,40,1,36,1,8,15,2,1,144,1,10,3,8,1,36,5,56,3,2,1,720,1,2,
%U A363520 21,8,5,36,1,8,3,70,1,1152,1,2,15,8,7,36,1,320,3,2,1
%N A363520 Product of the divisors of n that are < sqrt(n).
%F A363520 a(n) = Product_{d|n, d<sqrt(n)} d.
%F A363520 a(n) = Product_{k=1..floor(sqrt(n-1))} k^c(n/k), where c(m) = 1-ceiling(m)+floor(m).
%F A363520 a(n) = A072499(n)/A000196(n)^A010052(n) for n>=1.
%e A363520 The product of divisors of 16 that are < sqrt(16) = 4 is 1*2 = 2, so a(16) = 2.
%t A363520 a[n_] := Times @@ Select[Divisors[n], #^2 < n &]; Array[a, 100]
%o A363520 (PARI) a(n) = vecprod(select(x->(x^2<n), divisors(n))); \\ _Michel Marcus_, Jun 08 2023
%Y A363520 Cf. A000196, A010052, A072499, A363521.
%Y A363520 Cf. A070039 (sum of those divisors).
%K A363520 nonn,easy
%O A363520 1,6
%A A363520 _Wesley Ivan Hurt_, Jun 07 2023