A295165 - OEIS

%I #16 Oct 16 2020 06:28:06

%S 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,

%T 80,84,98,102,110,114,128,140,150,158,168,180,182,198,200,212,224,228,

%U 230,234,252,257,264,270,272,278,282,308,312,314,318,332,348,354,374,380,384,402,410,420,422,432

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

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

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

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

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

%H Robert Israel, <a href="/A295165/b295165.txt">Table of n, a(n) for n = 1..10000</a>

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

%p sf:= proc(n) option remember; n*procname(n-1)+(-1)^n end proc:

%p sf(0):= 1:

%p select(n -> igcd(sf(n),doublefactorial(n))=1, [$0..1000]);

%t Select[Range[0, 1000], CoprimeQ[Subfactorial[#], #!!]&] (* _Jean-François Alcover_, Oct 16 2020 *)

%Y Cf. A000166, A006882, A008864, A083318.

%K nonn

%O 1,3

%A _Robert Israel_, Nov 16 2017