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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.
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%I #13 Jan 24 2022 04:07:49

%S 1,12,147,57603,160797,4611243,36822513,878112417,2069618187,

%T 9891199227,9098192883,27885254943,73104587283,132014176203,

%U 3457814397303,1449081095007,5644476547437,9051074413563,31516441411377,8343886414773,5272121828883

%N 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 a(9) > 5*10^9. - _Jon E. Schoenfield_, Jan 13 2022

%e 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 N:= 10^9:

%p Q:= Vector(N,datatype=integer[4]):

%p P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]):

%p T:= Array(0..7): T[0]:= 1:

%p nP:= nops(P):

%p for i from 1 to nP do

%p for j from 1 to i do

%p v:= P[i]^2 + P[i]*P[j] + P[j]^2;

%p if v > N then break fi;

%p Q[v]:= Q[v]+1;

%p if T[Q[v]] = 0 or v < T[Q[v]] then T[Q[v]]:= v fi

%p od od:

%p convert(T,list);

%Y Cf. A349987.

%K nonn,more

%O 0,2

%A _J. M. Bergot_ and _Robert Israel_, Jan 09 2022

%E a(8) from _Jon E. Schoenfield_, Jan 13 2022

%E a(9)-a(20) from _Martin Ehrenstein_, Jan 24 2022