A116992 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.

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, 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, 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

Offset

1,12

Links

Diana Mecum, Table of n, a(n) for n = 1..1170

Example

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

Prog

(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

Crossrefs

Cf. A052248.

Sequence in context: A324116 A030757 A004592 * A233267 A090740 A094603

Adjacent sequences: A116989 A116990 A116991 * A116993 A116994 A116995

Keyword

nonn

Author

Leroy Quet, Apr 02 2006

Extensions

Corrected and extended by Diana L. Mecum, Jul 19 2008

Status

approved