OFFSET
1,16
COMMENTS
After a(1) = 1, a(n) is the number of factorizations of n with at least two factors, the largest two of which are equal.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
The initial terms count the following factorizations:
1: {}
4: 2*2
8: 2*2*2
9: 3*3
16: 2*2*2*2
16: 4*4
18: 2*3*3
25: 5*5
27: 3*3*3
32: 2*2*2*2*2
32: 2*4*4
36: 2*2*3*3
36: 6*6
48: 3*4*4
49: 7*7
50: 2*5*5
54: 2*3*3*3
64: 2*2*2*2*2*2
64: 2*2*4*4
64: 4*4*4
64: 8*8
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[facs[n], FreeQ[conj[#], 1]&]], {n, 1, 100}]
PROG
(PARI) A325045(n, m=n, facs=List([])) = if(1==n, (0==#facs || (#facs>=2 && facs[1]==facs[2])), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A325045(n/d, d, newfacs))); (s)); \\ Antti Karttunen, May 03 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 27 2019
EXTENSIONS
More terms from Antti Karttunen, May 03 2022
STATUS
approved