cp's OEIS Frontend

A318749 Number of pairwise relatively nonprime strict factorizations of n (no two factors are coprime).

%I A318749 #17 Oct 12 2018 04:42:56
%S A318749 1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,3,1,1,2,2,1,1,1,3,1,1,
%T A318749 1,3,1,1,1,3,1,1,1,2,2,1,1,5,1,2,1,2,1,3,1,3,1,1,1,3,1,1,2,4,1,1,1,2,
%U A318749 1,1,1,5,1,1,2,2,1,1,1,5,2,1,1,3,1,1,1,3,1,3,1,2,1,1,1,7,1,2,2,3,1,1,1,3,1
%N A318749 Number of pairwise relatively nonprime strict factorizations of n (no two factors are coprime).
%C A318749 a(n) depends only on prime signature of n (cf. A025487). - _Antti Karttunen_, Oct 08 2018
%H A318749 Antti Karttunen, <a href="/A318749/b318749.txt">Table of n, a(n) for n = 1..10000</a>
%H A318749 Antti Karttunen, <a href="/A318749/a318749.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%H A318749 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%e A318749 The a(96) = 7 factorizations are (96), (2*48), (4*24), (6*16), (8*12), (2*4*12), (2*6*8).
%e A318749 The a(480) = 18 factorizations:
%e A318749   (480)
%e A318749   (2*240) (4*120) (6*80) (8*60) (10*48) (12*40) (16*30) (20*24)
%e A318749   (2*4*60) (2*6*40) (2*8*30) (2*10*24) (2*12*20) (4*6*20) (4*10*12) (6*8*10)
%e A318749   (2*4*6*10)
%t A318749 strfacs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[strfacs[n/d],Min@@#1>d&],{d,Rest[Divisors[n]]}]];
%t A318749 Table[Length[Select[strfacs[n],And@@(GCD[##]>1&)@@@Select[Tuples[#,2],Less@@#&]&]],{n,50}]
%o A318749 (PARI) A318749(n, m=n, facs=List([])) = if(1==n, (1!=gcd(Vec(facs))), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs,d); s += A318749(n/d, d-1, newfacs))); (s)); \\ _Antti Karttunen_, Oct 08 2018
%Y A318749 Cf. A001055, A045778, A051185, A281116, A303282, A305843, A305854, A317748, A318715, A318717, A318721.
%K A318749 nonn
%O A318749 1,8
%A A318749 _Gus Wiseman_, Sep 02 2018
%E A318749 More terms from _Antti Karttunen_, Oct 08 2018