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 A325760 Heinz number of the frequency span of n. 3
 1, 2, 3, 12, 5, 72, 7, 40, 27, 120, 11, 864, 13, 168, 180, 112, 17, 1296, 19, 1440, 252, 264, 23, 2880, 75, 312, 135, 2016, 29, 1200, 31, 352, 396, 408, 420, 972, 37, 456, 468, 4800, 41, 1680, 43, 3168, 3240, 552, 47, 8064, 147, 3600, 612, 3744, 53, 6480, 660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k). We define the frequency span of an integer partition to be the partition itself if it has no or only one block, and otherwise it is the multiset union of the partition and the frequency span of its multiplicities. For example, the frequency span of (3,2,2,1) is {1,2,2,3} U {1,1,2} U {1,2} U {1,1} U {2} = {1,1,1,1,1,1,2,2,2,2,2,3}. The frequency span of a positive integer n is the frequency span of its prime indices (row n of A296150). LINKS MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; freqspan[ptn_]:=If[Length[ptn]<=1, ptn, Sort[Join[ptn, freqspan[Sort[Length/@Split[ptn]]]]]]; Table[Times@@Prime/@freqspan[primeMS[n]], {n, 30}] CROSSREFS Row-products of A325277. The prime indices of a(n) are row n of A325757. The unsorted prime signature of a(n) is row n of A325758. Cf. A001221, A001222, A056239, A071625, A112798, A181819, A182857, A323014, A324843, A325248, A325249, A325759. Sequence in context: A124444 A038610 A334313 * A056819 A124442 A220271 Adjacent sequences:  A325757 A325758 A325759 * A325761 A325762 A325763 KEYWORD nonn AUTHOR Gus Wiseman, May 19 2019 STATUS approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)