cp's OEIS Frontend

A319786 Number of factorizations of n where no two factors are relatively prime.

%I A319786 #15 Nov 09 2018 22:02:32
%S A319786 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,4,2,1,3,2,1,1,1,7,1,1,
%T A319786 1,4,1,1,1,4,1,1,1,2,2,1,1,7,2,2,1,2,1,4,1,4,1,1,1,3,1,1,2,11,1,1,1,2,
%U A319786 1,1,1,7,1,1,2,2,1,1,1,7,5,1,1,3,1,1,1,4,1,3,1,2,1,1,1,12,1,2,2,4,1,1,1,4,1
%N A319786 Number of factorizations of n where no two factors are relatively prime.
%C A319786 First differs from A305193 at a(36) = 4, A305193(36) = 5.
%C A319786 a(n) depends only on prime signature of n (cf. A025487). - _Antti Karttunen_, Nov 07 2018
%H A319786 Antti Karttunen, <a href="/A319786/b319786.txt">Table of n, a(n) for n = 1..11520</a>
%H A319786 Antti Karttunen, <a href="/A319786/a319786.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%H A319786 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%e A319786 The a(48) = 7 factorizations are (2*2*2*6), (2*2*12), (2*4*6), (2*24), (4*12), (6*8), (48).
%t A319786 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A319786 Table[Length[Select[facs[n],!Or@@CoprimeQ@@@Subsets[#,{2}]&]],{n,100}]
%o A319786 (PARI) A319786(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 += A319786(n/d, d, newfacs))); (s)); \\ _Antti Karttunen_, Nov 07 2018
%Y A319786 Cf. A001055, A007716, A045778, A049311, A162247, A281116, A283877, A305193, A305854, A306006, A316980, A318749.
%Y A319786 Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319782, A319789.
%K A319786 nonn
%O A319786 1,4
%A A319786 _Gus Wiseman_, Sep 27 2018
%E A319786 More terms from _Antti Karttunen_, Nov 07 2018