cp's OEIS Frontend

A285573 Number of finite nonempty sets of pairwise indivisible divisors of n.

%I A285573 #8 Apr 21 2017 20:43:25
%S A285573 1,2,2,3,2,5,2,4,3,5,2,9,2,5,5,5,2,9,2,9,5,5,2,14,3,5,4,9,2,19,2,6,5,
%T A285573 5,5,19,2,5,5,14,2,19,2,9,9,5,2,20,3,9,5,9,2,14,5,14,5,5,2,49,2,5,9,7,
%U A285573 5,19,2,9,5,19,2,34,2,5,9,9,5,19,2,20,5,5,2,49,5,5,5,14,2,49,5,9,5,5,5,27,2,9,9,19
%N A285573 Number of finite nonempty sets of pairwise indivisible divisors of n.
%C A285573 From _Robert Israel_, Apr 21 2017: (Start)
%C A285573 If n = p^k for prime p, a(n) = k+1.
%C A285573 If n = p^j*q^k for distinct primes p,q, a(n) = binomial(j+k+2,j+1)-1. (End)
%e A285573 The a(12)=9 sets are: {1}, {2}, {3}, {4}, {6}, {12}, {2,3}, {3,4}, {4,6}.
%p A285573 g:= proc(S) local x, Sx; option remember;
%p A285573    if nops(S) = 0 then return {{}} fi;
%p A285573    x:= S[1];
%p A285573    Sx:= subsop(1=NULL,S);
%p A285573    procname(Sx) union map(t -> t union {x}, procname(remove(s -> s mod x = 0 or x mod s = 0, Sx)))
%p A285573 end proc:
%p A285573 f:= proc(n) local F,D;
%p A285573   F:= ifactors(n)[2];
%p A285573   D:= numtheory:-divisors(mul(ithprime(i)^F[i,2],i=1..nops(F)));
%p A285573   nops(g(D)) - 1;
%p A285573 end proc:
%p A285573 map(f, [$1..100]); # _Robert Israel_, Apr 21 2017
%t A285573 nn=50;
%t A285573 stableSets[u_,Q_]:=If[Length[u]===0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r===w||Q[r,w]||Q[w,r]],Q]]]];
%t A285573 Table[Length[Rest[stableSets[Divisors[n],Divisible]]],{n,1,nn}]
%Y A285573 Cf. A006126, A048143, A076078, A076413, A198085, A285572.
%K A285573 nonn
%O A285573 1,2
%A A285573 _Gus Wiseman_, Apr 21 2017