A365078 - OEIS

A365078

a(n) is the least divisor (d) of prime(n)# such that prime(n)# / d + 1 is prime where p# denotes the product of all primes <= p.

1, 1, 1, 1, 1, 5, 5, 3, 13, 3, 1, 7, 11, 23, 7, 7, 13, 17, 21, 23, 47, 29, 5, 55, 85, 31, 21, 31, 11, 21, 23, 5, 57, 21, 97, 67, 11, 7, 41, 43, 29, 39, 11, 15, 89, 21, 11, 83, 47, 43, 85, 85, 17, 17, 11, 127, 177, 167, 15, 23, 21, 17, 67, 149, 113, 15, 131, 47, 61, 95, 53, 115, 31, 79, 1

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..75.

FORMULA

a(n) = prime(n)# / (A365021(n)-1).

Conjecture: a(n) < 2*prime(n).

PROG

(PARI) a(n) = my(P=vecprod(primes(n)), d=1); while(!ispseudoprime(floor((P/d)+1)) || gcd(P, d)<>d, d=d+2); d;

CROSSREFS

Cf. A002110, A365021.