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A317589 Heinz numbers of uniformly normal integer partitions. 3
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 23, 25, 27, 29, 30, 31, 32, 36, 37, 41, 43, 47, 49, 53, 59, 60, 61, 64, 67, 71, 73, 79, 81, 83, 89, 90, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 150, 151, 157, 163, 167, 169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

An integer partition is uniformly normal if either (1) it is of the form (x, x, ..., x) for some x > 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a uniformly normal integer partition.

LINKS

Table of n, a(n) for n=1..62.

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

uninrmQ[q_]:=Or[q=={}||Length[Union[q]]==1, And[Union[q]==Range[Max[q]], uninrmQ[Sort[Length/@Split[q], Greater]]]];

Select[Range[1000], uninrmQ[primeMS[#]]&]

CROSSREFS

Cf. A055932, A056239, A181819, A182850, A296150, A304687, A304818, A317089, A317090, A317245, A317246, A317492, A317588, A317590.

Sequence in context: A242413 A243068 A081061 * A141807 A246422 A072495

Adjacent sequences:  A317586 A317587 A317588 * A317590 A317591 A317592

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 01 2018

STATUS

approved

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Last modified March 19 19:30 EDT 2019. Contains 321330 sequences. (Running on oeis4.)