OFFSET
1,1
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.
EXAMPLE
Sequence of all non-uniformly normal integer partitions begins: (31), (41), (32), (311), (42), (51), (2111), (61), (411), (52), (71), (43), (81), (62), (3111), (421), (511), (322), (91), (21111), (331).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2018
STATUS
approved