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A343141 Numbers k such that k*A001414(k)+1 is the square of a prime. 2
8, 15, 36, 48, 112, 120, 280, 408, 456, 760, 1036, 1584, 1785, 1800, 1936, 2856, 3294, 3990, 4305, 4389, 14868, 18796, 19734, 21560, 29145, 30060, 30080, 30432, 33558, 36576, 45080, 47838, 52271, 54320, 78184, 78960, 82038, 90896, 98494, 99360, 109668, 110187, 114009, 117670, 127140, 132600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..450

EXAMPLE

a(3) = 36 is a term because A001414(36) = 2*2+2*3 = 10 and 36*10+1 = 361 = 19^2 where 19 is prime.

MAPLE

sopf:= proc(x) local t; add(t[1]*t[2], t=ifactors(x)[2]) end proc:

filter:= proc(n) local x;

   x:= n*sopf(n)+1;

   issqr(x) and isprime(sqrt(x))

end proc:

select(filter, [$1..10^5]);

MATHEMATICA

Select[Range[150000], PrimeQ@ Sqrt[#*Total@ Flatten[ConstantArray @@@ FactorInteger[#]] + 1] &] (* Michael De Vlieger, Apr 06 2021 *)

CROSSREFS

Cf. A001248, A001414.

Sequence in context: A287644 A089954 A134020 * A197602 A306599 A226151

Adjacent sequences:  A343137 A343138 A343139 * A343142 A343143 A343144

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Apr 06 2021

STATUS

approved

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Last modified June 22 00:27 EDT 2021. Contains 345367 sequences. (Running on oeis4.)