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A321649
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Irregular triangle whose n-th row is the conjugate of the integer partition with Heinz number n.
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16
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1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 2, 2, 2, 1, 1, 1
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OFFSET
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1,4
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1
1 1
2
1 1 1
2 1
1 1 1 1
3
2 2
2 1 1
1 1 1 1 1
3 1
1 1 1 1 1 1
2 1 1 1
2 2 1
4
1 1 1 1 1 1 1
3 2
1 1 1 1 1 1 1 1
3 1 1
2 2 1 1
2 1 1 1 1
1 1 1 1 1 1 1 1 1
The sequence of dual partitions begins: (), (1), (11), (2), (111), (21), (1111), (3), (22), (211), (11111), (31), (111111), (2111), (221), (4), (1111111), (32), (11111111), (311), (2211), (21111), (111111111), (41), (222), (211111), (33), (3111), (1111111111), (321).
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[conj[primeMS[n]], {n, 30}]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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