A343141 Numbers k such that k*A001414(k)+1 is the square of a prime.

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

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: A343138 A343139 A343140 * A343142 A343143 A343144

Keyword

nonn

Author

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

Status

approved