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 A302243 Total weight of the n-th twice-odd-factored multiset partition. 28
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS FORMULA a(n) = A302242(2n + 1). EXAMPLE 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)). MATHEMATICA 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}] CROSSREFS Cf. A003963, A007716, A034691, A048673,  A056239, A061775, A063834 A064216, A096443, A249620, A255397, A255906, A275024, A279789, A281113, A299757, A302242. Sequence in context: A309363 A280153 A023671 * A117535 A270747 A214517 Adjacent sequences:  A302240 A302241 A302242 * A302244 A302245 A302246 KEYWORD nonn AUTHOR Gus Wiseman, Apr 03 2018 STATUS approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)