A129843 - OEIS

A129843

a(n) = number of positive integers that are <= n and are coprime to n!! (n!! = A006882(n)).

1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 5, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 6, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 7, 6, 8, 6, 8, 6, 7, 6, 8, 6, 8, 6, 8, 7, 8, 7, 9, 7, 9, 7, 10, 7, 10, 7, 10, 7, 10, 7, 11

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OFFSET

1,3

LINKS

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

FORMULA

From Robert Israel, Dec 08 2022: (Start)

If n is odd, a(n) = A070939(n).

If n > 2 is even, a(n) = 1 + A056171(n). (End)

MAPLE

f:= proc(n) local t;

if n::odd then ilog2(n)+1

else 1+numtheory:-pi(n) - numtheory:-pi(n/2)

end proc:

f(2):= 1:

map(f, [$1..100]); # Robert Israel, Dec 08 2022

MATHEMATICA

a[n_]:=Module[{}, co=0; For[i=1, i<n+1, i++, If[GCD[n!!, i]==1, co++ ]]; co]; Table[a[n], {n, 1, 80}] (* Stefan Steinerberger, Jun 05 2007 *)

Table[Total[Boole[CoprimeQ[n!!, Range[n]]]], {n, 80}] (* Harvey P. Dale, Dec 12 2022 *)

CROSSREFS

Cf. A006882, A056171, A070939.

Sequence in context: A335458 A335454 A182745 * A349043 A330036 A050430

Adjacent sequences: A129840 A129841 A129842 * A129844 A129845 A129846

KEYWORD

nonn

AUTHOR

Leroy Quet, Jun 03 2007

EXTENSIONS

More terms from Stefan Steinerberger, Jun 05 2007

STATUS

approved