A316364 Number of factorizations of n into factors > 1 such that every distinct submultiset of the factors has a different average.
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 2, 5, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 6, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 8, 1, 2, 3, 4, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 6, 2, 2, 1, 9, 2, 2, 2, 5, 1, 9, 2, 3, 2, 2, 2, 10, 1, 3, 3, 5, 1, 5, 1, 5, 4
Offset: 1
Keywords
Examples
The a(80) = 6 factorizations are (80), (10*8), (16*5), (20*4), (40*2), (10*4*2).
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Crossrefs
Programs
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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}] -
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
Extensions
More terms from Antti Karttunen, Sep 21 2018
Comments