cp's OEIS Frontend

A129139 a(n) = number of positive integers which are coprime to n and are <= d(n), where d(n) = A000005(n).

%I A129139 #21 Mar 27 2025 06:11:53
%S A129139 1,1,2,2,2,1,2,2,2,2,2,2,2,2,3,3,2,2,2,2,3,2,2,3,3,2,3,3,2,2,2,3,3,2,
%T A129139 4,3,2,2,3,3,2,2,2,3,3,2,2,3,3,2,3,3,2,3,4,3,3,2,2,3,2,2,4,4,4,3,2,3,
%U A129139 3,2,2,4,2,2,3,3,4,3,2,4,4,2,2,3,4,2,3,4,2,3,4,3,3,2,4,4,2,3,4,4,2,3,2,4,4
%N A129139 a(n) = number of positive integers which are coprime to n and are <= d(n), where d(n) = A000005(n).
%H A129139 Antti Karttunen, <a href="/A129139/b129139.txt">Table of n, a(n) for n = 1..16384</a>
%F A129139 a(n) = Sum_{d|n} mu(d)*floor(tau(n)/d). - _Ridouane Oudra_, Mar 26 2025
%e A129139 d(16) = 5. So a(16) is the number of integers coprime to 16 which are <= 5. There are 3 such integers: 1, 3, 5; so a(16) = 3.
%p A129139 with(numtheory): a:=proc(n) local ct,j: ct:=0: for j from 1 to tau(n) do if gcd(j,n)=1 then ct:=ct+1 else fi od: ct; end: seq(a(n),n=1..140); # _Emeric Deutsch_, Apr 02 2007
%t A129139 A129139[n_] := Count[CoprimeQ[Range[DivisorSigma[0, n]], n], True];
%t A129139 Array[A129139, 100] (* _Paolo Xausa_, Mar 27 2025 *)
%o A129139 (PARI) A129139(n) = sum(k=1,numdiv(n),(1==gcd(k,n))); \\ _Antti Karttunen_, Apr 01 2021
%Y A129139 Cf. A000005, A129138, A126131, A074919.
%K A129139 nonn
%O A129139 1,3
%A A129139 _Leroy Quet_, Mar 30 2007
%E A129139 More terms from _Emeric Deutsch_, Apr 02 2007