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
Keywords
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
Programs
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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
Extensions
Extended by Ray Chandler, Jun 24 2008
Comments