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A302243
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Total weight of the n-th twice-odd-factored multiset partition.
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32
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0, 1, 1, 2, 2, 1, 2, 2, 1, 3, 3, 2, 2, 3, 2, 1, 2, 3, 3, 3, 1, 2, 3, 2, 4, 2, 4, 2, 4, 1, 3, 4, 3, 1, 3, 3, 2, 3, 3, 2, 4, 1, 2, 3, 4, 4, 2, 4, 2, 3, 2, 3, 4, 3, 1, 4, 3, 3, 4, 3, 2, 2, 3, 1, 3, 5, 5, 4, 2, 2, 3, 3, 3, 5, 2, 4, 3, 2, 1, 5, 4, 2, 3, 2, 4, 5, 4, 4
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OFFSET
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0,4
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COMMENTS
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A multiset partition is a finite multiset of finite nonempty multisets of positive integers. The n-th twice-odd-factored multiset partition is constructed by factoring 2n + 1 into prime numbers and then factoring each prime index into prime numbers and taking their prime indices.
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LINKS
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FORMULA
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EXAMPLE
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Sequence of multiset partitions begins: (), ((1)), ((2)), ((11)), ((1)(1)), ((3)), ((12)), ((1)(2)), ((4)), ((111)), ((1)(11)), ((22)), ((2)(2)), ((1)(1)(1)), ((13)), ((5)), ((1)(3)), ((2)(11)), ((112)), ((1)(12)), ((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[Sum[PrimeOmega[k], {k, primeMS[2n-1]}], {n, 100}]
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CROSSREFS
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Cf. A003963, A007716, A034691, A048673, A056239, A061775, A063834 A064216, A096443, A249620, A255397, A255906, A275024, A279789, A281113, A299757, A302242.
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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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