OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
9: {2,2}
15: {2,3}
27: {2,2,2}
45: {2,2,3}
75: {2,3,3}
81: {2,2,2,2}
105: {2,3,4}
135: {2,2,2,3}
225: {2,2,3,3}
243: {2,2,2,2,2}
315: {2,2,3,4}
375: {2,3,3,3}
405: {2,2,2,2,3}
525: {2,3,3,4}
675: {2,2,2,3,3}
729: {2,2,2,2,2,2}
735: {2,3,4,4}
945: {2,2,2,3,4}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Select[Range[100], normQ[primeMS[#]-1]&]
CROSSREFS
The version starting at 1 is A055932.
The partitions with these Heinz numbers are counted by A264396.
Positions of 1's in A339662.
A000009 counts partitions covering an initial interval.
A000070 counts partitions with a selected part.
A016945 lists numbers with smallest prime index 2.
A034296 counts gap-free (or flat) partitions.
A073491 lists numbers with gap-free prime indices.
A325240 lists numbers with smallest prime multiplicity 2.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 20 2021
STATUS
approved