%I #10 Jun 01 2024 22:07:11
%S 1,2,3,4,5,4,7,8,9,7,11,9,13,10,13,16,17,13,19,17,19,16,23,20,25,19,
%T 27,24,29,19,31,32,29,25,34,31,37,28,35,36,41,27,43,38,42,34,47,41,49,
%U 38,45,45,53,40,53,51,51,43,59,45,61,46,60,64,63,43,67,59,61,50,71,65,73
%N Number of integers in {1, 2, ..., sigma(n)} that are coprime to n.
%C Compare the definition of a(n) to phi(n) = number of integers in {1, 2, ..., n} that are coprime to n.
%F a(n) = Sum_{d|n} mu(d)*floor(sigma(n)/d). - _Ridouane Oudra_, May 12 2024
%e There are four numbers in {1, 2, ..., sigma(4) = 7} that are coprime to 4, i.e. 1, 3, 5, 7. Hence a(4) = 4.
%p with(numtheory): seq(add(mobius(d)*floor(sigma(n)/d), d in divisors(n)), n=1..100) ; # _Ridouane Oudra_, May 12 2024
%t h[n_] := Module[{l}, l = {}; For[i = 1, i <= DivisorSigma[1, n], i++, If[GCD[i, n] == 1, l = Append[l, i]]]; l]; Table[Length[h[i]], {i, 1, 100}]
%Y Cf. A000203.
%K nonn
%O 1,2
%A _Joseph L. Pe_, Oct 04 2002