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A316364 Number of factorizations of n into factors > 1 such that every distinct submultiset of the factors has a different average. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A099042 A140774 A056924 * 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

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)