login
As n runs through composite numbers, a(n) = number of nonprime d < n such that gcd(d,n) = 1.
1

%I #13 Oct 25 2019 21:19:58

%S 1,1,1,3,2,1,2,4,3,1,2,6,4,1,12,5,10,5,1,6,11,7,15,3,8,14,6,2,8,12,10,

%T 3,28,7,19,11,4,26,10,22,14,2,14,20,15,32,5,15,27,8,6,17,21,17,41,6,

%U 12,33,20,4,43,21,35,19,3,50,22,38,24,50,10,19,37

%N As n runs through composite numbers, a(n) = number of nonprime d < n such that gcd(d,n) = 1.

%C It appears that a(n) = A048864(A002808(n)). - _Michel Marcus_, Jul 14 2013

%F a(n) = A048983(n) + 1. - _Michel Marcus_, Jul 14 2013

%e 9 is 4th composite number, gcd(9,1) = gcd(9,4) = gcd(9,8) = 1, so a(4) = 3.

%o (PARI) ai(nn) = {forcomposite (n=1, nn, nb = 0; for(d=1, n-1, if (! isprime(d) && gcd(n, d) == 1, nb++)); print1(nb, ", "););} \\ _Michel Marcus_, Jul 14 2013

%Y Cf. A000010, A048983, A002808.

%K easy,nonn

%O 1,4

%A _Naohiro Nomoto_