A294925 a(n) is the smallest number k with n prime factors such that p + k/p is prime for every prime p | k.
2, 6, 30, 210, 15810, 292110, 16893030, 984016110, 17088913842, 2446241358990, 1098013758964122
Offset: 1
Examples
a(2) = 6 because k = 2*3 = 6 is the smallest number with 2 prime factors such that 2 + 6/2 = 3 + 6/3 = 5 is prime. From _Michael De Vlieger_, Nov 13 2017: (Start) First differences of prime indices of a(n): n a(n) A287352(a(n)) ---------------------------------------------------------- 1 2 1 2 6 1, 1 3 30 1, 1, 1, 4 210 1, 1, 1, 1 5 15810 1, 1, 1, 4, 4 6 292110 1, 1, 1, 1, 2, 22 7 16893030 1, 1, 1, 1, 1, 15, 7 8 984016110 1, 1, 1, 1, 1, 5, 2, 66 9 17088913842 1, 1, 2, 1, 1, 1, 1, 1, 67 10 2446241358990 1, 1, 1, 2, 1, 2, 2, 3, 1, 93 11 1098013758964122 1, 1, 2, 1, 1, 3, 2, 8, 3, 22, 10 (End)
Crossrefs
Cf. A293756.
Programs
-
PARI
isok(k, n) = {if (!issquarefree(k), return (0)); if (omega(k) != n, return (0)); fordiv(k, d, if (isprime(d) && !isprime(d+k/d), return(0));); return (1);} a(n) = {my(k=1); while( !isok(k, n), k++); k;} \\ Michel Marcus, Nov 11 2017
Extensions
a(5)-a(7) from Michel Marcus, Nov 11 2017
a(8) from Michel Marcus, Nov 12 2017
a(9)-a(10) from Michael De Vlieger, Nov 13 2017
a(11) (and update of table in Example section) from Jon E. Schoenfield, Nov 19 2017
Comments