A316365 Number of factorizations of n into factors > 1 such that every distinct subset of the factors has a different sum.
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, 4, 1, 6, 2, 2, 2, 9, 1, 2, 2, 7, 1, 5, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 7, 2, 2, 1, 10, 1, 2, 4, 9, 2, 5, 1, 4, 2, 4, 1, 14, 1, 2, 4, 4, 2, 5, 1, 11, 5, 2, 1, 9, 2, 2, 2, 7, 1, 10, 2, 4, 2, 2, 2, 15, 1, 4, 4, 9, 1, 5, 1, 7, 5
Offset: 1
Keywords
Examples
The a(24) = 7 factorizations are (2*2*2*3), (2*2*6), (2*3*4), (2*12), (3*8), (4*6), (24). The a(54) = 6 factorizations are (2*3*3*3), (2*3*9), (2*27), (3*18), (6*9), (54).
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10080
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
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@@Total/@Union[Subsets[#]]&]],{n,100}] -
PARI
primeprodbybits(v,b) = { my(m=1,i=1); while(b>0,if(b%2, m *= prime(v[i])); i++; b >>= 1); (m); }; sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); }; all_distinct_subsets_have_different_sums(v) = { my(m=Map(),s,pp); for(i=0,(2^#v)-1, pp = primeprodbybits(v,i); s = sumbybits(v,i); if(mapisdefined(m,s), if(mapget(m,s)!=pp, return(0)), mapput(m,s,pp))); (1); }; A316365(n, m=n, facs=List([])) = if(1==n, all_distinct_subsets_have_different_sums(Vec(facs)), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs,d); s += A316365(n/d, d, newfacs))); (s)); \\ Antti Karttunen, Oct 08 2018
Extensions
More terms from Antti Karttunen, Oct 08 2018
Comments