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Numbers k such that k divides the number of planar partitions of k (A000219).
1

%I #18 Mar 02 2018 06:21:10

%S 1,3,6,8,10,281,382,590,5135,13897,31387,37045,46199,85057

%N Numbers k such that k divides the number of planar partitions of k (A000219).

%C a(15) > 10^5. - _Seiichi Manyama_, Feb 11 2018

%C Next term, if it exists, is greater than 250000. - _Vaclav Kotesovec_, Mar 02 2018

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>

%e 281 is in the sequence because A000219(281) = 126261896396707768167577329446424334 is divisible by 281.

%t pp[0] = 1; pp[n_] := pp[n] = (1/n)*Sum[pp[n-k]*DivisorSigma[2, k], {k, 1, n}]; Reap[For[n = 0; k = 1, k < 10^5, k++, If[Divisible[pp[k], k], n++; Print["a(", n, ") = ", k, " pp(", k, ") = ", pp[k]]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Feb 11 2018 *)

%Y Cf. A000219, A051177, A056848.

%K nonn,more

%O 1,2

%A _Ilya Gutkovskiy_, Feb 09 2018

%E a(14) from _Seiichi Manyama_, Feb 11 2018