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A376664 Least number k such that there are A376663(n) partitions x_1 + ... + x_j = k such that the multinomial coefficient k!/(x_1! * ... * x_j!) is equal to n, i.e., the first row k of A036038 in which n appears A376663(n) times (or 0 if n = 0).

%I A376664 #6 Oct 02 2024 14:23:57
%S A376664 0,2,3,4,5,3,7,8,9,5,11,4,13,14,6,16,17,18,19,5,7,22,23,4,25,26,27,8,
%T A376664 29,5,31,32,33,34,7,9,37,38,39,40,41,7,43,44,10,46,47,48,49,50,51,52,
%U A376664 53,54,11,8,57,58,59,5,61,62,63,64,65,12,67,68,69,8,71
%N A376664 Least number k such that there are A376663(n) partitions x_1 + ... + x_j = k such that the multinomial coefficient k!/(x_1! * ... * x_j!) is equal to n, i.e., the first row k of A036038 in which n appears A376663(n) times (or 0 if n = 0).
%C A376664 Differs from A376368 at n = 1260, 2520, 5040, 60060, 83160, ... . For example, 1260 appears first in row A376368(1260) = 7 of A036038, but only once. It also appears once in row 9, but in row a(1260) = 10 it appears A376663(1260) = 2 times.
%C A376664 a(n) <= n, with equality if and only if n is not in A325472.
%H A376664 Pontus von Brömssen, <a href="/A376664/b376664.txt">Table of n, a(n) for n = 1..10000</a>
%H A376664 Pontus von Brömssen, <a href="/plot2a?name1=A000027&amp;name2=A376664&amp;tform1=log+base+10&amp;tform2=log+base+10&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Log-log plot</a>, using Plot2.
%Y A376664 Cf. A036038, A325472, A376368, A376663.
%K A376664 nonn
%O A376664 1,2
%A A376664 _Pontus von Brömssen_, Oct 02 2024