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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No odd integer has any non-isolated divisors.
LINKS
FORMULA
a(n) = A007955(2n) / A134338(2n). - Ray Chandler, Jun 24 2008
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A205030 A278250 A357441 * A162299 A281552 A205506
KEYWORD
nonn
AUTHOR
Leroy Quet, Oct 21 2007
EXTENSIONS
Extended by Ray Chandler, Jun 24 2008
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)