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A295165 Numbers n such that !n and n!! (A000166(n) and A006882(n)) are coprime. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 16 2020 *)

CROSSREFS

Cf. A000166, A006882, A008864, A083318.

Sequence in context: A165707 A052063 A129525 * A258023 A190232 A084693

Adjacent sequences:  A295162 A295163 A295164 * A295166 A295167 A295168

KEYWORD

nonn

AUTHOR

Robert Israel, Nov 16 2017

STATUS

approved

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Last modified July 24 01:41 EDT 2021. Contains 346269 sequences. (Running on oeis4.)