OFFSET
1,1
COMMENTS
The enumeration of these partitions by sum is given by A325199.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
5: {3}
8: {1,1,1}
14: {1,4}
21: {2,4}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
35: {3,4}
36: {1,1,2,2}
40: {1,1,1,3}
54: {1,2,2,2}
56: {1,1,1,4}
66: {1,2,5}
98: {1,4,4}
99: {2,2,5}
110: {1,3,5}
120: {1,1,1,2,3}
125: {3,3,3}
132: {1,1,2,5}
MATHEMATICA
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
Select[Range[1000], otbmax[primeptn[#]]-otb[primeptn[#]]==2&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved