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A137326 a(n) = sqrt(A139033(n)).

%I A137326 #12 Feb 12 2023 05:37:03
%S A137326 1,2,6,24,36,42,48,66,78,126,138,144,162,210,264,276,288,294,336,390,
%T A137326 420,462,498,504,510,534,540,570,618,630,642,660,690,702,744,780,840,
%U A137326 882,906,984,1002,1008,1020,1044,1050,1086,1140,1176,1188,1278,1290,1308
%N A137326 a(n) = sqrt(A139033(n)).
%p A137326 s:= proc(n) option remember; `if`(n<1, 0, a(n)^2+s(n-1)) end:
%p A137326 a:= proc(n) option remember; local k, m;
%p A137326       k:= s(n-1); for m from 1+a(n-1)
%p A137326       while not isprime(k+m^2) do od; m
%p A137326     end: a(1):=1:
%p A137326 seq(a(n), n=1..52);  # _Alois P. Heinz_, Jan 26 2023
%t A137326 s[n_] := s[n] = If[n < 1, 0, a[n]^2 + s[n-1]];
%t A137326 a[n_] := a[n] = Module[{k, m}, k = s[n-1]; For[m = 1 + a[n-1], !PrimeQ[k + m^2], m++]; m];
%t A137326 a[1] = 1;
%t A137326 Table[a[n], {n, 1, 52}] (* _Jean-François Alcover_, Feb 12 2023, after _Alois P. Heinz_ *)
%Y A137326 Cf. A139033.
%K A137326 nonn
%O A137326 1,2
%A A137326 _Zak Seidov_, Apr 07 2008