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

%I

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

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

%C Numbers n such that 2*A000720(n) = A000010(n) + A001221(n). - _Max Alekseyev_, Aug 22 2013

%C 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

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

%o (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

%K nonn,fini,full

%O 1,1

%A _Naohiro Nomoto_

%E More terms from _Michel Marcus_, Jul 14 2013

%E Keywords fini, full added by _Max Alekseyev_, Oct 29 2019

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)