OFFSET
1,2
COMMENTS
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
16: {1,1,1,1}
20: {1,1,3}
30: {1,2,3}
32: {1,1,1,1,1}
56: {1,1,1,4}
64: {1,1,1,1,1,1}
90: {1,2,2,3}
128: {1,1,1,1,1,1,1}
140: {1,1,3,4}
176: {1,1,1,1,5}
210: {1,2,3,4}
256: {1,1,1,1,1,1,1,1}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
norqQ[m_]:=Sort[m]==Range[0, Max[m]];
msubs[s_]:=Join@@@Tuples[Table[Take[t, i], {t, Split[s]}, {i, 0, Length[t]}]];
Select[Range[1000], norqQ[Total/@Select[msubs[primeMS[#]], SameQ@@#&]]&]
CROSSREFS
These partitions are counted by A353865.
A073093 counts prime-power divisors.
A353832 represents the operation of taking run-sums of a partition.
A353836 counts partitions by number of distinct run-sums.
A353863 counts partitions whose weak run-sums cover an initial interval.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 07 2022
STATUS
approved