OFFSET
1,2
COMMENTS
EXAMPLE
The terms together with their prime indices begin:
1: {}
3: {2}
7: {4}
13: {6}
21: {2,4}
37: {12}
39: {2,6}
89: {24}
133: {4,8}
117: {2,2,6}
111: {2,12}
273: {2,4,6}
351: {2,2,2,6}
For example, the choices for a(12) = 273 are:
{1,1,1} {1,2,2} {2,2,2}
{1,1,2} {1,2,3} {2,2,3}
{1,1,3} {1,2,6} {2,2,6}
{1,1,6} {1,4,6} {2,4,6}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
az=Table[Length[Select[Tuples[Divisors/@primeMS[n]], LessEqual@@#&]], {n, 1000}];
Table[Position[az, k][[1, 1]], {k, mnrm[az]}]
CROSSREFS
Positions of first appearances in A355735.
The case of prime factors instead of divisors is counted by A355745.
The decreasing version is counted by A355749.
A000005 counts divisors.
A003963 multiplies together the prime indices of n.
A120383 lists numbers divisible by all of their prime indices.
A324850 lists numbers divisible by the product of their prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2022
STATUS
approved