OFFSET
1,3
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, Cartesian product.
EXAMPLE
The a(15) = 4 choices are: (1,1), (1,3), (2,1), (2,3).
The a(18) = 4 choices are: (1,1,1), (1,1,2), (1,2,1), (1,2,2).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Times@@Length/@Divisors/@primeMS[n], {n, 100}]
CROSSREFS
Positions of 1's are A000079.
Positions of first appearances are A355732.
Choosing divisors of each of 1..n and resorting gives A355747.
An ordered version (using standard order compositions) is A355748.
A000005 counts divisors.
A003963 multiplies together the prime indices of n.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
A324850 lists numbers divisible by the product of their prime indices.
A340852 lists numbers that can be factored into divisors of bigomega.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2022
STATUS
approved