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.

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, 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, 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

Offset: 1

Author

Leroy Quet, Oct 21 2007

Keywords

• nonn

Comments

No odd integer has any non-isolated divisors.

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007955, A134338.

Programs

Mathematica

pnid[n_]:=With[{d=Divisors[2n]},Times@@Select[d,MemberQ[d,#+1] || MemberQ[ d,#-1]&]]; Array[pnid,100] (* Harvey P. Dale, Jul 07 2020 *)

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

Formula

a(n) = A007955(2n) / A134338(2n). - Ray Chandler, Jun 24 2008

Extensions

Extended by Ray Chandler, Jun 24 2008