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

%I A295165 #16 Oct 16 2020 06:28:06
%S A295165 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 A295165 80,84,98,102,110,114,128,140,150,158,168,180,182,198,200,212,224,228,
%U A295165 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 A295165 Numbers n such that !n and n!! (A000166(n) and A006882(n)) are coprime.
%C A295165 Odd n is in the sequence iff !n is not divisible by any odd primes < n.
%C A295165 Even n is in the sequence iff !n is not divisible by any odd primes < n/2.
%C A295165 All odd terms are in A083318, all even terms > 2 are in A008864, but both of these are strict inclusions.
%C A295165 Odd terms include 1,3,5,9,17,33,65,257,513,32769.
%H A295165 Robert Israel, <a href="/A295165/b295165.txt">Table of n, a(n) for n = 1..10000</a>
%e A295165 !5 = 44 and 5!! = 15 are coprime so 5 is in the sequence.
%p A295165 sf:= proc(n) option remember; n*procname(n-1)+(-1)^n end proc:
%p A295165 sf(0):= 1:
%p A295165 select(n -> igcd(sf(n),doublefactorial(n))=1, [$0..1000]);
%t A295165 Select[Range[0, 1000], CoprimeQ[Subfactorial[#], #!!]&] (* _Jean-François Alcover_, Oct 16 2020 *)
%Y A295165 Cf. A000166, A006882, A008864, A083318.
%K A295165 nonn
%O A295165 1,3
%A A295165 _Robert Israel_, Nov 16 2017