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A266325 Smallest integer m such that there is a partition of m with product of multiplicities of parts equal to n.

%I A266325 #40 Dec 21 2016 06:38:45
%S A266325 0,2,3,4,5,6,7,8,9,9,11,10,13,11,11,12,17,12,19,13,13,15,23,14,15,17,
%T A266325 15,15,29,16,31,16,17,21,17,17,37,23,19,18,41,19,43,19,19,27,47,20,21,
%U A266325 20,23,21,53,21,21,21,25,33,59,22,61,35,22,22,23,23,67,25
%N A266325 Smallest integer m such that there is a partition of m with product of multiplicities of parts equal to n.
%H A266325 Alois P. Heinz, <a href="/A266325/b266325.txt">Table of n, a(n) for n = 1..2500</a>
%F A266325 a(n) = min { m >= 0 : A266477(m,n) > 0 }.
%F A266325 p in primes => a(p) = p.
%p A266325 b:= proc(n, i, p) option remember; `if`(n=0, `if`(p=1, 1, 0),
%p A266325       `if`(i<1, 0, b(n, i-1, p)+add(`if`(irem(p, j)=0,
%p A266325        b(n-i*j, i-1, p/j), 0), j=1..n/i)))
%p A266325     end:
%p A266325 a:= proc(n) option remember; local m;
%p A266325       if isprime(n) then return n fi;
%p A266325       for m from 0 do if b(m$2, n)>0 then return m fi od
%p A266325     end:
%p A266325 seq(a(n), n=1..100);
%t A266325 b[n_, i_, p_] := b[n, i, p] = If[n == 0, If[p == 1, 1, 0], If[i < 1, 0, b[n, i - 1, p] + Sum[If[Mod[p, j] == 0, b[n - i*j, i - 1, p/j], 0], {j, 1, n/i}]]]; a[n_] := a[n] = Module[{m}, If[PrimeQ[n], Return[n]]; For[m = 0, True, m++, If[b[m, m, n] > 0, Return[m]]]]; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Dec 21 2016, translated from Maple *)
%Y A266325 Cf. A266477.
%K A266325 nonn
%O A266325 1,2
%A A266325 _Emeric Deutsch_ and _Alois P. Heinz_, Jan 04 2016