OFFSET
1,12
LINKS
Wikipedia, Coprime integers.
FORMULA
a(n) = A000688(n) if n is nonprime, otherwise a(n) = 0.
EXAMPLE
The a(n) factorizations for n = 6, 12, 24, 36, 48, 72, 96:
2*3 3*4 3*8 4*9 3*16 8*9 3*32
2*2*3 2*3*4 2*2*9 2*3*8 2*4*9 3*4*8
2*2*2*3 3*3*4 3*4*4 3*3*8 2*3*16
2*2*3*3 2*2*3*4 2*2*2*9 2*2*3*8
2*2*2*2*3 2*3*3*4 2*3*4*4
2*2*2*3*3 2*2*2*3*4
2*2*2*2*2*3
MATHEMATICA
ufacs[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[ufacs[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
Table[Length[Select[ufacs[Select[Divisors[n], PrimePowerQ[#]&], n], GCD@@#<=1&]], {n, 100}]
CROSSREFS
For pairwise coprime instead of relatively prime we have A143731.
The version for partitions instead of factorizations is A356067.
A000005 counts divisors.
A001055 counts factorizations.
A001222 counts prime-power divisors.
A289509 lists numbers whose prime indices are relatively prime.
A295935 counts twice-factorizations with constant blocks (type PPR).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2022
STATUS
approved