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%I #18 Jun 17 2023 14:22:48
%S 1,2,3,2,5,3,7,4,3,5,11,8,13,7,5,8,17,12,19,10,7,11,23,18,5,13,9,14,
%T 29,20,31,16,11,17,7,27,37,19,13,32,41,36,43,22,27,23,47,36,7,25,17,
%U 26,53,36,11,32
%N a(n) = greatest product < n of some subset of the divisors of n, or if n is in A008578 then a(n) = n.
%C a(n) = n <=> n in A008578.
%C For composite n, a(n) < n < A363501(n) and where both bounds are products of divisors of n and as tight as possible.
%e 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]; the maximal product that is lesser than 4 is 2, so a(4) = 2.
%t If[PrimeQ@n || n == 1, n,
%t Last@Select[Union[Times @@@ Subsets[Divisors@n]], # < n &]];
%o (PARI) a(n) = my(d=divisors(n), nb = #d, m=1); forsubset(nb, s, my(p=vecprod(vector(#s, k, d[s[k]]))); if (p<n, m=max(m, p))); if (m>1, m, n); \\ _Michel Marcus_, Jun 17 2023
%Y Cf. A008578, A363501.
%K nonn
%O 1,2
%A _Denis Ivanov_, Jun 12 2023
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