A048984 As n runs through composite numbers, a(n) = number of nonprime d < n such that gcd(d,n) = 1.
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, 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, 12, 33, 20, 4, 43, 21, 35, 19, 3, 50, 22, 38, 24, 50, 10, 19, 37
Offset: 1
Examples
9 is 4th composite number, gcd(9,1) = gcd(9,4) = gcd(9,8) = 1, so a(4) = 3.
Programs
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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
Formula
a(n) = A048983(n) + 1. - Michel Marcus, Jul 14 2013
Comments