OFFSET
1,2
COMMENTS
LINKS
Wikipedia, Coprime integers.
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
6: {1,2}
9: {2,2}
15: {2,3}
49: {4,4}
35: {3,4}
27: {2,2,2}
45: {2,2,3}
98: {1,4,4}
63: {2,2,4}
105: {2,3,4}
171: {2,2,8}
117: {2,2,6}
81: {2,2,2,2}
135: {2,2,2,3}
For example, the choices for a(12) = 105 are:
(1,1,1) (1,3,2) (2,1,4)
(1,1,2) (1,3,4) (2,3,1)
(1,1,4) (2,1,1) (2,3,2)
(1,3,1) (2,1,2) (2,3,4)
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]], GCD@@#==1&]], {n, 100}];
Table[Position[az+1, k][[1, 1]], {k, mnrm[az+1]}]
CROSSREFS
Positions of first appearances in A355737.
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 21 2022
STATUS
approved