cp's OEIS Frontend

A323436 Number of plane partitions whose parts are the prime indices of n.

%I A323436 #4 Jan 15 2019 18:45:43
%S A323436 1,1,1,1,2,1,2,1,3,2,2,1,3,1,2,2,5,1,4,1,3,2,2,1,5,2,2,3,3,1,4,1,7,2,
%T A323436 2,2,8,1,2,2,5,1,4,1,3,3,2,1,7,2,4,2,3,1,7,2,5,2,2,1,8,1,2,3,11,2,4,1,
%U A323436 3,2,4,1,12,1,2,4,3,2,4,1,7,5,2,1,8,2,2
%N A323436 Number of plane partitions whose parts are the prime indices of n.
%C A323436 Number of ways to fill a Young diagram with the prime indices of n such that all rows and columns are weakly decreasing.
%C A323436 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A323436 The a(120) = 12 plane partitions:
%e A323436   32111
%e A323436 .
%e A323436   311   321   3111   3211
%e A323436   21    11    2      1
%e A323436 .
%e A323436   31   32   311   321
%e A323436   21   11   2     1
%e A323436   1    1    1     1
%e A323436 .
%e A323436   31   32
%e A323436   2    1
%e A323436   1    1
%e A323436   1    1
%e A323436 .
%e A323436   3
%e A323436   2
%e A323436   1
%e A323436   1
%e A323436   1
%t A323436 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A323436 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323436 ptnplane[n_]:=Union[Map[Reverse@*primeMS,Join@@Permutations/@facs[n],{2}]];
%t A323436 Table[Length[Select[ptnplane[y],And[And@@GreaterEqual@@@#,And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]],{y,100}]
%Y A323436 Cf. A000085, A000219, A003293, A056239, A112798, A114736, A117433, A138178, A296188, A299968.
%Y A323436 Cf. A323300, A323429, A323437, A323438, A323439.
%K A323436 nonn
%O A323436 0,5
%A A323436 _Gus Wiseman_, Jan 15 2019