OFFSET
1,2
COMMENTS
First differs from A066312 in having 1 and lacking 462.
First differs from A104210 in having 1 and lacking 42.
A part x is neighborless iff neither x - 1 nor x + 1 are parts.
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.
EXAMPLE
The terms together with their prime indices begin:
1: {}
6: {1,2}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
24: {1,1,1,2}
30: {1,2,3}
35: {3,4}
36: {1,1,2,2}
45: {2,2,3}
48: {1,1,1,1,2}
54: {1,2,2,2}
60: {1,1,2,3}
72: {1,1,1,2,2}
75: {2,3,3}
77: {4,5}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Function[ptn, !Or@@Table[!MemberQ[ptn, x-1]&&!MemberQ[ptn, x+1], {x, Union[ptn]}]]@*primeMS]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2022
STATUS
approved