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

1,1

Comments

Such k is an even squarefree number.

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..11.

Example

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)

Prog

(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

Crossrefs

Cf. A293756.

Sequence in context: A375534 A077176 A101178 * A091456 A354411 A293756

Adjacent sequences: A294922 A294923 A294924 * A294926 A294927 A294928

Keyword

nonn,more

Author

Thomas Ordowski, 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

Status

approved