A049012 Composite numbers n such that number of nonprime d with 0 < d < n, gcd(n,d)=1, is pi(n).

33, 75, 94, 106, 118, 1540, 2442, 5340

Offset: 1

Author

Naohiro Nomoto

Keywords

• nonn
• fini
• full

Comments

Numbers n such that 2*A000720(n) = A000010(n) + A001221(n). - Max Alekseyev, Aug 22 2013

The sequence is finite since the l.h.s. grows as 2n/log(n), while the r.h.s. is asymptotically at least A080130*n/log(log(n)). In fact, known bounds for A000720 and A000010 imply that there are no terms above 10^7, and thus the sequence is full. - Max Alekseyev, Oct 29 2019

Examples

			gcd(33,d)=1: d=1,4,8,10,14,16,20,25,26,28,32, pi(33)=11, so 33 is a term.
		

Programs

PARI

isok(n) = {if (isprime(n) , return (0)); nb = 0; for (d=1, n-1, if (! isprime(d) && gcd(n, d) == 1, nb++);); return (nb == primepi(n));} \\ Michel Marcus, Jul 14 2013

Extensions

More terms from Michel Marcus, Jul 14 2013

Keywords fini, full added by Max Alekseyev, Oct 29 2019