cp's OEIS Frontend

A134339 a(n) = product of the positive "non-isolated divisors" of (2n). A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

%I A134339 #15 Jul 07 2020 15:59:05
%S A134339 2,2,6,2,2,24,2,2,6,40,2,24,2,2,180,2,2,24,2,40,252,2,2,24,2,2,6,112,
%T A134339 2,720,2,2,6,2,2,1728,2,2,6,40,2,1008,2,2,16200,2,2,24,2,40,6,2,2,24,
%U A134339 220,112,6,2,2,720,2,2,252,2,2,3168,2,2,6,40,2,1728,2,2,180,2,2,3744,2,40,6
%N A134339 a(n) = product of the positive "non-isolated divisors" of (2n). A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.
%C A134339 No odd integer has any non-isolated divisors.
%H A134339 Harvey P. Dale, <a href="/A134339/b134339.txt">Table of n, a(n) for n = 1..1000</a>
%F A134339 a(n) = A007955(2n) / A134338(2n). - _Ray Chandler_, Jun 24 2008
%e A134339 The divisors of 2*10 = 20 are 1,2,4,5,10,20. Of these, 1,2,4,5 are the non-isolated divisors. So a(10) = 1*2*4*5 = 40.
%t A134339 pnid[n_]:=With[{d=Divisors[2n]},Times@@Select[d,MemberQ[d,#+1] || MemberQ[ d,#-1]&]]; Array[pnid,100] (* _Harvey P. Dale_, Jul 07 2020 *)
%o A134339 (PARI) a(n) = {my(c=1, k=2*n, x=1); fordiv(k, d, if(d==c+1 || k%(d+1)==0, x*=d); c=d); x; } \\ _Jinyuan Wang_, Mar 12 2020
%Y A134339 Cf. A007955, A134338.
%K A134339 nonn
%O A134339 1,1
%A A134339 _Leroy Quet_, Oct 21 2007
%E A134339 Extended by _Ray Chandler_, Jun 24 2008