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A376368 Least number k with a partition k = x_1 + ... + x_j such that the multinomial coefficient k!/(x_1! * ... * x_j!) is equal to n.

%I A376368 #16 Sep 23 2024 11:32:30
%S A376368 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 A376368 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 A376368 53,54,11,8,57,58,59,5,61,62,63,64,65,12,67,68,69,8,71
%N A376368 Least number k with a partition k = x_1 + ... + x_j such that the multinomial coefficient k!/(x_1! * ... * x_j!) is equal to n.
%C A376368 Index of first row of A078760 (or A036038 when n >= 2) that contains n.
%C A376368 a(n) <= n, with equality if and only if n is in A376371, i.e., if and only if n is not in A325472.
%H A376368 Pontus von Brömssen, <a href="/A376368/b376368.txt">Table of n, a(n) for n = 1..10000</a>
%H A376368 Pontus von Brömssen, <a href="/plot2a?name1=A000027&amp;name2=A376368&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.
%F A376368 a(k!) = k for k != 1.
%e A376368 a(6) = 3, because 6 appears in row 3 of A078760, corresponding to the multinomial coefficient 3!/(1!*1!*1!) = 6.
%Y A376368 Cf. A036038, A078760, A325472, A376369, A376370, A376371.
%K A376368 nonn
%O A376368 1,2
%A A376368 _Pontus von Brömssen_, Sep 22 2024