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%I #23 Jul 31 2019 20:55:38
%S 1,2,3,11,4,9,5,11,14,9,6,21,28,10,7,15,54,21,20,58,10,8,32,21,24,28,
%T 14,11,26,9,44,66,16,94,18,21,86,47,129,66,35,10,27,15,14,75,56,70,19,
%U 74,178,62,52,340,18,11,20,26,54,124,115,101,24,66,84,21,47,94,32,19
%N a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.
%C The initial term could also be taken to be 0.
%C From the formula a(p(n)) = n, it follows that every positive integer appears in this sequence. - _Franklin T. Adams-Watters_, Feb 09 2016
%H M. F. Hasler, <a href="/A046641/b046641.txt">Table of n, a(n) for n = 1..20000</a>.
%H M. F. Hasler, <a href="http://www.univ-ag.fr/~mhasler/oeis/A046641.c">A046641.c - C program for fast computation of a(n) for large values of n.</a> [From _M. F. Hasler_, Oct 18 2008]
%F a(p(n)) = n. - _Franklin T. Adams-Watters_, Feb 09 2016
%e The first partition number divisible by 9 is p(14) = 135, so a(9) = 14.
%t Table[SelectFirst[Range[10^3], Divisible[PartitionsP@ #, n] &], {n, 70}] (* _Michael De Vlieger_, Feb 10 2016, Version 10 *)
%o (PARI) a(n) = my(m = 1); while(numbpart(m) % n, m++); m; \\ _Michel Marcus_, Feb 10 2016
%Y Cf. A000041, A040051.
%Y See A091690 for simple PARI code, A145523(n)=a(2^n), A145524(n)=a(10^n), A145771 for record values. [_M. F. Hasler_, Oct 18 2008]
%K nonn
%O 1,2
%A _David W. Wilson_
%E Definition corrected by _Max Alekseyev_, Apr 25 2010
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