cp's OEIS Frontend

A363501 a(n) = smallest product > n of some subset of the divisors of n, or if no product > n exists then a(n) = n.

%I A363501 #28 Jun 17 2023 14:22:44
%S A363501 1,2,3,8,5,12,7,16,27,20,11,18,13,28,45,32,17,27,19,40,63,44,23,32,
%T A363501 125,52,81,56,29,36,31,64,99,68,175,48,37,76,117,50,41,63,43,88,75,92,
%U A363501 47,64,343,100,153,104,53,81,275,64,171,116,59,72,61,124,147
%N A363501 a(n) = smallest product > n of some subset of the divisors of n, or if no product > n exists then a(n) = n.
%C A363501 a(n) = n iff n=1 or n is prime.
%C A363501 For composite n, A363627(n) < n < a(n) and where both bounds are products of divisors of n and as tight as possible.
%e A363501 n = 4; divisors: [1,2,4]; subsets: [[], [1], [2], [4], [1, 2], [1, 4], [2, 4], [1, 2, 4]]; products: [1, 1, 2, 4, 2, 4, 8, 8]; minimal product that greater than 4 is 8, so a(4) = 8.
%e A363501 n = 5; divisors: [1,5]; subsets: [[], [1], [5], [1, 5]]; products: [1, 1, 5, 5]; no products greater than 5, so a(5) = 5.
%t A363501 a[n_] := If[PrimeQ@n || n == 1, n,
%t A363501   First@Select[Union[Times @@@ Subsets[Divisors@n]], # > n &]];
%o A363501 (PARI) a(n) = my(d=divisors(n), nb = #d, m=oo); forsubset(nb, s, my(p=vecprod(vector(#s, k, d[s[k]]))); if (p>n, m=min(m, p))); if (m<oo, m, n); \\ _Michel Marcus_, Jun 17 2023
%Y A363501 Cf. A027750, A363627.
%K A363501 nonn
%O A363501 1,2
%A A363501 _Denis Ivanov_, Jun 06 2023