OFFSET
1,36
COMMENTS
Also the number of multiset partitions of the multiset of prime indices of n with no constant parts.
LINKS
EXAMPLE
The a(840) = 11 factorizations are (6*10*14), (6*140), (10*84), (12*70), (14*60), (15*56), (20*42), (21*40), (24*35), (28*30), (840).
MATHEMATICA
acfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[acfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], !PrimePowerQ[#]&]}]];
Table[Length[acfacs[n]], {n, 100}]
PROG
(PARI) A322452(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&(1<omega(d)), s += A322452(n/d, d))); (s)); \\ Antti Karttunen, Jan 03 2019
(PARI) first(n) = my(res=vector(n)); for(i=1, n, f=factor(i); v=vecsort(f[, 2] , , 4); f[, 2] = v; fb = factorback(f); if(fb==i, res[i] = A322452(i), res[i] = res[fb])); res \\ A322452 the function above \\ David A. Corneth, Jan 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2018
EXTENSIONS
More terms from Antti Karttunen, Jan 03 2019
STATUS
approved