A323436 - OEIS

A323436

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

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, 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, 3, 2, 4, 1, 12, 1, 2, 4, 3, 2, 4, 1, 7, 5, 2, 1, 8, 2, 2

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OFFSET

0,5

COMMENTS

Number of ways to fill a Young diagram with the prime indices of n such that all rows and columns are weakly decreasing.

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.

LINKS

Table of n, a(n) for n=0..86.

EXAMPLE

The a(120) = 12 plane partitions:

32111

311 321 3111 3211

21 11 2 1

31 32 311 321

21 11 2 1

1 1 1 1

31 32

2 1

1 1

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

ptnplane[n_]:=Union[Map[Reverse@*primeMS, Join@@Permutations/@facs[n], {2}]];

Table[Length[Select[ptnplane[y], And[And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, 100}]

CROSSREFS

Cf. A000085, A000219, A003293, A056239, A112798, A114736, A117433, A138178, A296188, A299968.

Cf. A323300, A323429, A323437, A323438, A323439.

Sequence in context: A008481 A318473 A127669 * A056692 A331600 A039637

Adjacent sequences: A323433 A323434 A323435 * A323437 A323438 A323439

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 15 2019

STATUS

approved