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A294925 a(n) is the smallest number k with n prime factors such that p + k/p is prime for every prime p | k.

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%I A294925 #22 Jan 15 2021 23:08:44
%S A294925 2,6,30,210,15810,292110,16893030,984016110,17088913842,2446241358990,
%T A294925 1098013758964122
%N A294925 a(n) is the smallest number k with n prime factors such that p + k/p is prime for every prime p | k.
%C A294925 Such k is an even squarefree number.
%C A294925 Conjecture: the sequence is infinite.
%e A294925 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.
%e A294925 From _Michael De Vlieger_, Nov 13 2017: (Start)
%e A294925 First differences of prime indices of a(n):
%e A294925    n              a(n)  A287352(a(n))
%e A294925   ----------------------------------------------------------
%e A294925    1                2   1
%e A294925    2                6   1, 1
%e A294925    3               30   1, 1, 1,
%e A294925    4              210   1, 1, 1, 1
%e A294925    5            15810   1, 1, 1, 4, 4
%e A294925    6           292110   1, 1, 1, 1, 2, 22
%e A294925    7         16893030   1, 1, 1, 1, 1, 15, 7
%e A294925    8        984016110   1, 1, 1, 1, 1,  5, 2, 66
%e A294925    9      17088913842   1, 1, 2, 1, 1,  1, 1,  1, 67
%e A294925   10    2446241358990   1, 1, 1, 2, 1,  2, 2,  3,  1, 93
%e A294925   11 1098013758964122   1, 1, 2, 1, 1,  3, 2,  8,  3, 22, 10
%e A294925 (End)
%o A294925 (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);}
%o A294925 a(n) = {my(k=1); while( !isok(k, n), k++); k;} \\ _Michel Marcus_, Nov 11 2017
%Y A294925 Cf. A293756.
%K A294925 nonn,more
%O A294925 1,1
%A A294925 _Thomas Ordowski_, Nov 11 2017
%E A294925 a(5)-a(7) from _Michel Marcus_, Nov 11 2017
%E A294925 a(8) from _Michel Marcus_, Nov 12 2017
%E A294925 a(9)-a(10) from _Michael De Vlieger_, Nov 13 2017
%E A294925 a(11) (and update of table in Example section) from _Jon E. Schoenfield_, Nov 19 2017