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A323436
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Number of plane partitions whose parts are the prime indices of n.
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17
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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
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0,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The a(120) = 12 plane partitions:
32111
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311 321 3111 3211
21 11 2 1
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31 32 311 321
21 11 2 1
1 1 1 1
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31 32
2 1
1 1
1 1
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3
2
1
1
1
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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