A343142 a(n) = sqrt(k*A001414(k)+1) for k in A343141.

7, 11, 19, 23, 41, 41, 71, 103, 113, 151, 223, 199, 239, 199, 241, 307, 487, 379, 491, 419, 1063, 1777, 1013, 881, 1741, 2339, 1409, 3169, 1597, 2287, 1471, 2143, 5009, 2521, 5393, 2351, 3389, 2393, 2663, 2161, 2887, 2969, 4271, 3361, 4889, 2549, 10177, 3191, 3499, 16631, 2753, 10243, 4481, 3691

Offset

1,1

Comments

Primes that occur more than once in the sequence include 41, 199, 4159, 9437, 10687, 16561, 31249, 40591, 64601, 67339, 91631, 93889, 96799, 111871, 122201, 145417, 180847, 911201.

Links

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

Formula

a(n) = sqrt(A343141(n)*A001414(A343141(n))+1).

Example

a(3) = 19 because A343141(3) = 36 and sqrt(36*A001414(36)+1) = 19.

Maple

sopf:= proc(x) local t; add(t[1]*t[2], t=ifactors(x)[2]) end proc:
g:= proc(n) local x, y;
x:= n*sopf(n)+1;
  if issqr(x) then
  y:= sqrt(x);
  if isprime(y) then return y fi
  fi
end proc:
map(g, [$1..10^5]);

Mathematica

Block[{f}, f[n_] := Sqrt[n*Total@ Flatten[ConstantArray @@@ FactorInteger[n]] + 1]; f /@ Select[Range[200000], PrimeQ@ f[#] &] ] (* Michael De Vlieger, Apr 06 2021 *)

Crossrefs

Cf. A001414, A343141.

Sequence in context: A129899 A129842 A065312 * A235727 A370010 A141337

Adjacent sequences: A343139 A343140 A343141 * A343143 A343144 A343145

Keyword

nonn

Author

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

Status

approved