OFFSET
1,2
COMMENTS
EXAMPLE
The a(n) counted divisors of n = 1, 2, 4, 6, 12, 16, 24, 30, 36, 48, 72, 90:
1 2 4 6 12 16 24 30 36 48 72 90
1 2 3 6 8 12 15 18 24 36 45
1 2 4 4 8 6 12 16 24 30
1 3 2 6 5 9 12 18 18
2 1 4 3 6 8 12 15
1 3 2 4 6 9 9
2 1 3 4 8 6
1 2 3 6 5
1 2 4 3
1 3 2
2 1
1
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
nogapQ[m_]:=m=={}||Union[m]==Range[Min[m], Max[m]];
Table[Length[Select[Divisors[n], nogapQ[primeMS[#]]&]], {n, 100}]
CROSSREFS
The initial case is A356224.
The complement in the initial case is counted by A356225.
A000005 counts divisors.
A001223 lists the prime gaps.
A328338 has third-largest divisor prime.
A356226 gives the lengths of maximal gapless intervals of prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 28 2022
STATUS
approved