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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
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).
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.
Sequence in context: A124444 A038610 A334313 * A056819 A124442 A220271
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2019
STATUS
approved