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A321747
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Sum of coefficients of elementary symmetric functions in the monomial symmetric function of the integer partition with Heinz number n.
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1
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1, 1, -1, 1, 1, -2, -1, 1, 1, 2, 1, -3, -1, -2, -2, 1, 1, 3, -1, 3, 2, 2, 1, -4, 1, -2, -1, -3, -1, -6, 1, 1, -2, 2, -2, 6, -1, -2, 2, 4, 1, 6, -1, 3, 3, 2, 1, -5, 1, 3, -2, -3, -1, -4, 2, -4, 2, -2, 1, -12, -1, 2, -3, 1, -2, -6, 1, 3, -2, -6, -1, 10, 1, -2
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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 sum of coefficients of m(2211) = 9e(6) + e(42) - 4e(51) is a(36) = 6.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[(-1)^(Total[primeMS[n]]-PrimeOmega[n])*Length[Permutations[primeMS[n]]], {n, 50}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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