OFFSET
1,1
COMMENTS
The enumeration of these partitions by sum is given by A325191.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
4: {1,1}
9: {2,2}
10: {1,3}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
20: {1,1,3}
42: {1,2,4}
45: {2,2,3}
50: {1,3,3}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
75: {2,3,3}
84: {1,1,2,4}
90: {1,2,2,3}
100: {1,1,3,3}
105: {2,3,4}
126: {1,2,2,4}
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[#]]==1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved