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A215111 Numbers n such that n^2+1 divides n!!. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is even.

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

LINKS

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

FORMULA

n such that A002522(n) | A006882(n)

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

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)