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 A285573 Number of finite nonempty sets of pairwise indivisible divisors of n. 45

%I

%S 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 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 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 Number of finite nonempty sets of pairwise indivisible divisors of n.

%C From _Robert Israel_, Apr 21 2017: (Start)

%C If n = p^k for prime p, a(n) = k+1.

%C If n = p^j*q^k for distinct primes p,q, a(n) = binomial(j+k+2,j+1)-1. (End)

%e The a(12)=9 sets are: {1}, {2}, {3}, {4}, {6}, {12}, {2,3}, {3,4}, {4,6}.

%p g:= proc(S) local x, Sx; option remember;

%p if nops(S) = 0 then return {{}} fi;

%p x:= S[1];

%p Sx:= subsop(1=NULL,S);

%p procname(Sx) union map(t -> t union {x}, procname(remove(s -> s mod x = 0 or x mod s = 0, Sx)))

%p end proc:

%p f:= proc(n) local F,D;

%p F:= ifactors(n)[2];

%p D:= numtheory:-divisors(mul(ithprime(i)^F[i,2],i=1..nops(F)));

%p nops(g(D)) - 1;

%p end proc:

%p map(f, [\$1..100]); # _Robert Israel_, Apr 21 2017

%t nn=50;

%t 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 Table[Length[Rest[stableSets[Divisors[n],Divisible]]],{n,1,nn}]

%Y Cf. A006126, A048143, A076078, A076413, A198085, A285572.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 21 2017

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Last modified August 3 04:30 EDT 2020. Contains 336197 sequences. (Running on oeis4.)