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A321648
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Number of permutations of the conjugate of the integer partition with Heinz number n.
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19
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1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 3, 1, 1, 2, 1, 3, 6, 5, 1, 2, 1, 6, 1, 4, 1, 6, 1, 1, 10, 7, 4, 2, 1, 8, 15, 3, 1, 12, 1, 5, 3, 9, 1, 2, 1, 3, 21, 6, 1, 2, 10, 4, 28, 10, 1, 6, 1, 11, 6, 1, 20, 20, 1, 7, 36, 12, 1, 2, 1, 12, 3, 8, 5, 30, 1, 3, 1, 13
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OFFSET
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1,6
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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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The a(42) = 12 permutations: (3211), (3121), (3112), (2311), (2131), (2113), (1321), (1312), (1231), (1213), (1132), (1123).
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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[Length[Permutations[conj[primeMS[n]]]], {n, 50}]
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PROG
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(PARI)
A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ From A008480
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
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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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