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A350655 a(n) is the least positive number that can be written as p^2 + p*q + q^2 in exactly n ways where p and q are primes and p <= q.

%I A350655 #13 Jan 24 2022 04:07:49
%S A350655 1,12,147,57603,160797,4611243,36822513,878112417,2069618187,
%T A350655 9891199227,9098192883,27885254943,73104587283,132014176203,
%U A350655 3457814397303,1449081095007,5644476547437,9051074413563,31516441411377,8343886414773,5272121828883
%N A350655 a(n) is the least positive number that can be written as p^2 + p*q + q^2 in exactly n ways where p and q are primes and p <= q.
%C A350655 a(9) > 5*10^9. - _Jon E. Schoenfield_, Jan 13 2022
%e A350655 a(3) = 57603 as 57603 has the three representations 57603 = 2^2 + 2*239 + 239^2 = 31^2 + 31*223 + 223^2 = 101^2 + 101*173 + 173^2 and no smaller number has this property.
%p A350655 N:= 10^9:
%p A350655 Q:= Vector(N,datatype=integer[4]):
%p A350655 P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]):
%p A350655 T:= Array(0..7): T[0]:= 1:
%p A350655 nP:= nops(P):
%p A350655 for i from 1 to nP do
%p A350655   for j from 1 to i do
%p A350655     v:= P[i]^2 + P[i]*P[j] + P[j]^2;
%p A350655     if v > N then break fi;
%p A350655     Q[v]:= Q[v]+1;
%p A350655     if T[Q[v]] = 0 or v < T[Q[v]] then T[Q[v]]:= v fi
%p A350655 od od:
%p A350655 convert(T,list);
%Y A350655 Cf. A349987.
%K A350655 nonn,more
%O A350655 0,2
%A A350655 _J. M. Bergot_ and _Robert Israel_, Jan 09 2022
%E A350655 a(8) from _Jon E. Schoenfield_, Jan 13 2022
%E A350655 a(9)-a(20) from _Martin Ehrenstein_, Jan 24 2022