A134339 - OEIS

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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, 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

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

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

Cf. A007955, A134338.

Sequence in context: A205030 A278250 A357441 * A162299 A281552 A205506

Adjacent sequences: A134336 A134337 A134338 * A134340 A134341 A134342

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 21 2007

EXTENSIONS

Extended by Ray Chandler, Jun 24 2008

STATUS

approved