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

1,3

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A000166, A006882, A008864, A083318.

Sequence in context: A052063 A129525 A351987 * A258023 A190232 A084693

Adjacent sequences: A295162 A295163 A295164 * A295166 A295167 A295168

Keyword

nonn

Author

Robert Israel, Nov 16 2017

Status

approved