OFFSET
1,2
COMMENTS
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i.
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
20: {1,1,3}
42: {1,2,4}
45: {2,2,3}
105: {2,3,4}
110: {1,3,5}
125: {3,3,3}
176: {1,1,1,1,5}
182: {1,4,6}
231: {2,4,5}
245: {3,4,4}
312: {1,1,1,2,6}
374: {1,5,7}
396: {1,1,2,2,5}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}];
Select[Range[100], PrimeOmega[#]==ats[primeMS[#]]&]
CROSSREFS
These partitions are counted by A357189.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 01 2022
STATUS
approved