OFFSET
1,6
COMMENTS
Note that such a factorization is necessarily strict.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
The a(80) = 6 factorizations are (80), (10*8), (16*5), (20*4), (40*2), (10*4*2).
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], UnsameQ@@Mean/@Union[Subsets[#]]&]], {n, 50}]
PROG
(PARI)
choosebybits(v, m) = { my(s=vector(hammingweight(m)), i=j=1); while(m>0, if(m%2, s[j] = v[i]; j++); i++; m >>= 1); s; };
hasdupavgs(v) = { my(avgs=Map(), k); for(i=1, (2^(#v))-1, k = (vecsum(choosebybits(v, i))/hammingweight(i)); if(mapisdefined(avgs, k), return(i), mapput(avgs, k, i))); (0); };
A316364(n, m=n, facs=List([])) = if(1==n, (0==hasdupavgs(Vec(facs))), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A316364(n/d, d, newfacs))); (s)); \\ Antti Karttunen, Sep 21 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 30 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 21 2018
STATUS
approved