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

1,6

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

Cf. A001055, A108917, A275972, A276024, A284640, A292886, A293627, A294150, A316313, A316314, A316365.

Sequence in context: A345345 A056924 A342083 * A318357 A323091 A045778

Adjacent sequences: A316361 A316362 A316363 * A316365 A316366 A316367

Keyword

nonn

Author

Gus Wiseman, Jun 30 2018

Extensions

More terms from Antti Karttunen, Sep 21 2018

Status

approved