login
A322452
Number of factorizations of n into factors > 1 not including any prime powers.
15
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1
OFFSET
1,36
COMMENTS
Also the number of multiset partitions of the multiset of prime indices of n with no constant parts.
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
Positions of 0's are the prime powers A000961.
Sequence in context: A352822 A090418 A363877 * A076754 A346482 A364043
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2018
EXTENSIONS
More terms from Antti Karttunen, Jan 03 2019
STATUS
approved