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A355643
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Numbers k having a divisor d such that d+k/d is prime.
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2
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1, 2, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 66, 70, 72, 76, 78, 82, 84, 88, 90, 96, 100, 102, 106, 108, 112, 114, 118, 120, 126, 130, 132, 136, 138, 142, 148, 150, 154, 156, 160, 162, 166, 168, 172, 174, 178, 180, 184, 186, 190, 192, 196, 198, 202, 204, 208
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OFFSET
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1,2
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COMMENTS
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All terms > 2 are congruent to 0 or 4 (mod 6).
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LINKS
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EXAMPLE
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a(10) = 24 is a term because 24 = 3*8 with 3+8 = 11 prime.
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MAPLE
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filter:= proc(n) local F, t;
F:= select(t -> t^2 <=n, numtheory:-divisors(n));
ormap(isprime, map(t -> t+n/t, F))
end proc:
select(filter, [$1..300]);
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MATHEMATICA
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q[n_] := AnyTrue[Divisors[n], PrimeQ[# + n/#] &]; Select[Range[200], q] (* Amiram Eldar, Jul 11 2022 *)
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PROG
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(PARI) isok(k) = fordiv(k, d, if (isprime(d+k/d), return(1))); \\ Michel Marcus, Jul 11 2022
(Python)
from sympy import divisors, isprime
def ok(n): return any(isprime(d+n//d) for d in divisors(n, generator=True))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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