A295165 Numbers n such that !n and n!! (A000166(n) and A006882(n)) are coprime.

0, 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 18, 20, 24, 30, 32, 33, 44, 48, 54, 62, 65, 68, 72, 74, 80, 84, 98, 102, 110, 114, 128, 140, 150, 158, 168, 180, 182, 198, 200, 212, 224, 228, 230, 234, 252, 257, 264, 270, 272, 278, 282, 308, 312, 314, 318, 332, 348, 354, 374, 380, 384, 402, 410, 420, 422, 432

Offset: 1

Author

Robert Israel, Nov 16 2017

Keywords

• nonn

Comments

Odd n is in the sequence iff !n is not divisible by any odd primes < n.

Even n is in the sequence iff !n is not divisible by any odd primes < n/2.

All odd terms are in A083318, all even terms > 2 are in A008864, but both of these are strict inclusions.

Odd terms include 1,3,5,9,17,33,65,257,513,32769.

Examples

			!5 = 44 and 5!! = 15 are coprime so 5 is in the sequence.
		

Links

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

Crossrefs

Cf. A000166, A006882, A008864, A083318.

Programs

Maple

sf:= proc(n) option remember; n*procname(n-1)+(-1)^n end proc:
sf(0):= 1:
select(n -> igcd(sf(n),doublefactorial(n))=1, [$0..1000]);

Mathematica

Select[Range[0, 1000], CoprimeQ[Subfactorial[#], #!!]&] (* Jean-François Alcover, Oct 16 2020 *)