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