OFFSET
1,6
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.
LINKS
Wikipedia, Coprime integers.
EXAMPLE
The a(2) = 1 through a(18) = 4 choices:
1 1 11 1 11 1 111 11 11 1 111 1 11 11 1111 1 111
12 12 13 112 12 13 112
21 14 21 121
23 122
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Tuples[Divisors/@primeMS[n]], GCD@@#==1&]], {n, 100}]
CROSSREFS
Positions of first appearances are A355738.
A000005 counts divisors.
A001222 counts prime factors with multiplicity.
A003963 multiplies together the prime indices of n.
A120383 lists numbers divisible by all of their prime indices.
A289508 gives GCD of prime indices.
A324850 lists numbers divisible by the product of their prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2022
STATUS
approved