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%I #17 Oct 08 2018 18:11:20
%S 1,1,1,2,1,2,1,2,2,2,1,3,1,2,2,3,1,3,1,3,2,2,1,4,2,2,2,3,1,5,1,2,2,2,
%T 2,6,1,2,2,4,1,5,1,3,3,2,1,5,2,3,2,3,1,4,2,4,2,2,1,8,1,2,3,4,2,5,1,3,
%U 2,5,1,6,1,2,3,3,2,5,1,5,3,2,1,8,2,2,2,4,1,8,2,3,2,2,2,6,1,3,3,6,1,5,1,4,5
%N Number of factorizations of n whose distinct factors are pairwise indivisible and greater than 1.
%H Antti Karttunen, <a href="/A305149/b305149.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A305149/a305149.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%e The a(60) = 8 factorizations are (2*2*3*5), (2*2*15), (3*4*5), (3*20), (4*15), (5*12), (6*10), (60). Missing from this list are (2*3*10), (2*5*6), (2*30).
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t Table[Length[Select[facs[n],Select[Tuples[Union[#],2],UnsameQ@@#&&Divisible@@#&]=={}&]],{n,100}]
%o (PARI)
%o pairwise_indivisible(v) = { for(i=1,#v,for(j=i+1,#v,if(!(v[j]%v[i]),return(0)))); (1); };
%o A305149(n, m=n, facs=List([])) = if(1==n, pairwise_indivisible(Set(facs)), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs,d); s += A305149(n/d, d, newfacs))); (s)); \\ _Antti Karttunen_, Oct 08 2018
%Y Cf. A001055, A001970, A007716, A034444, A045778, A259936, A281116, A285572, A302242, A303386, A303431, A305001, A305148, A305150.
%K nonn
%O 1,4
%A _Gus Wiseman_, May 26 2018
%E More terms from _Antti Karttunen_, Oct 08 2018
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