OFFSET
1,1
COMMENTS
We define a difference of a partition to be a difference of two adjacent parts.
EXAMPLE
The terms together with their prime indices begin:
20: (3,1,1)
28: (4,1,1)
40: (3,1,1,1)
44: (5,1,1)
52: (6,1,1)
56: (4,1,1,1)
63: (4,2,2)
68: (7,1,1)
76: (8,1,1)
80: (3,1,1,1,1)
84: (4,2,1,1)
88: (5,1,1,1)
92: (9,1,1)
99: (5,2,2)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Select[Range[100], (Min@@Differences[Reverse[primeMS[#]]]<-1)&&(Min@@Differences[conj[primeMS[#]]]<-1)&]
CROSSREFS
Heinz number rankings are in parentheses below.
These partitions are counted by A350839.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 26 2022
STATUS
approved