A215111 Numbers k such that k^2+1 divides k!!.

70, 132, 182, 212, 216, 242, 268, 278, 294, 302, 342, 360, 378, 394, 408, 438, 500, 512, 524, 538, 560, 568, 580, 606, 616, 660, 682, 684, 746, 748, 772, 776, 788, 798, 818, 822, 850, 882, 914, 922, 924, 948, 970, 1032, 1034, 1048, 1068, 1084, 1118, 1148, 1168

Offset

1,1

Comments

a(n) is even.

Even numbers k such that k^2+1 divides (k/2)!. - Robert Israel, Jun 19 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

k such that A002522(k) | A006882(k).

Example

70 is in the sequence because 70^2+1 = 4901 = 29*13^2 divides 70!! = 355044260642859198243475901411974413130137600000000 =
  2^67 * 3^15 * 5^8 * 7^5 * 11^3 * 13^2 * 17^2 *19 * 23 * 29 * 31.

Maple

with(numtheory):for n from 1 to 1300 do:x:=irem(doublefactorial(n), n^2+1): if x=0 then printf(`%d, `, n):else fi:od:

Mathematica

Select[Range[1200], Divisible[#!!, #^2+1]&] (* Harvey P. Dale, Oct 14 2015 *)

Crossrefs

Cf. A002522, A006882, A120416.

Sequence in context: A254367 A113928 A160354 * A255801 A044193 A044574

Adjacent sequences: A215108 A215109 A215110 * A215112 A215113 A215114

Keyword

nonn,easy

Author

Michel Lagneau, Aug 03 2012

Status

approved