A116992 - OEIS

%I #13 Mar 01 2015 16:49:41

%S 0,0,0,0,0,0,0,0,1,0,1,3,1,4,1,3,0,4,3,0,4,9,6,6,0,4,10,0,6,4,9,11,6,

%T 10,0,2,15,17,6,16,0,5,0,19,2,13,14,25,5,3,13,0,12,23,23,15,0,24,28,

%U 12,12,20,20,3,31,22,31,27,7,0,32,32,7,6,37,36,34,40,14,20,0,33,0,19,0,40

%N Number of primes < (highest prime dividing any composite between the n-th and (n+1)th prime) that are coprime to every composite between the n-th and (n+1)th prime.

%H Diana Mecum, <a href="/A116992/b116992.txt">Table of n, a(n) for n = 1..1170</a>

%e Between the 12th prime and the 13th prime are the composites 38, 39 and 40.

%e Dividing these composites are the primes 2, 3, 5, 13 and 19. There are three primes < 19 and coprime to the composites between 37 and 41: 7, 11 and 17. So a(12) = 3.

%o (PARI) a(n) = {p = prime(n); q = prime(n+1); vp = []; for (x=p+1, q-1, f = factor(x); for (i=1, #f~, vp = Set(concat(vp, f[i, 1])));); if (#vp == 0, return (0)); nb = 0; forprime (pp=2, precprime(vecmax(vp)-1), ok = 1; for (x=p+1, q-1, if (gcd(x, pp) != 1, ok = 0; break;);); if (ok, nb++);); nb;} \\ _Michel Marcus_, Mar 01 2015

%Y Cf. A052248.

%K nonn

%O 1,12

%A _Leroy Quet_, Apr 02 2006

%E Corrected and extended by _Diana L. Mecum_, Jul 19 2008