A248712 -id:A248712 - cp's OEIS frontend

A131574 Numbers n that are the product of two distinct odd primes and x^2 + y^2 = n has integer solutions.

65, 85, 145, 185, 205, 221, 265, 305, 365, 377, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 745, 785, 793, 865, 901, 905, 949, 965, 985, 1037, 1073, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1345, 1385, 1405, 1417, 1465, 1469

Offset: 1

Colin Barker, Aug 28 2007, corrected Aug 29 2007

nonn

The two primes are of the form 4*k + 1.

			65 is in the sequence because x^2 + y^2 = 65 = 5*13 has solutions (x,y) = (1,8), (4,7), (7,4) and (8,1).

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)

Cf. A000415, A121387, A248649, A248712, A264498, A264499

dop(d, nmax) = {
  my(L=List(), v=vector(d,m,1)~, f);
  for(n=1, nmax,
    f=factorint(n);
    if(#f~==d && f[1,1]>2 && f[,2]==v && f[,1]%4==v, listput(L, n))
  );
  Vec(L)
}
dop(2, 3000) \\ Colin Barker, Nov 15 2015

A248649 Numbers n that are the product of three distinct primes such that x^2+y^2 = n has integer solutions.

Original entry on oeis.org

130, 170, 290, 370, 410, 442, 530, 610, 730, 754, 890, 962, 970, 986, 1010, 1066, 1090, 1105, 1130, 1258, 1370, 1378, 1394, 1490, 1570, 1586, 1730, 1802, 1810, 1885, 1898, 1930, 1970, 2074, 2146, 2290, 2314, 2330, 2378, 2405, 2410, 2465, 2482, 2522, 2570

Offset: 1

Colin Barker, Oct 12 2014

nonn

Union of 2*A131574 and A264498. - Ray Chandler, Dec 09 2019

			130 is in the sequence because 130 = 2*5*13, and x^2+y^2=130 has integer solutions (x,y) = (3,11) and (7,9).
1105 is in the sequence because x^2 + y^2 = 1105 = 5*13*17 has solutions (x,y) = (4,33), (9,32), (12,31) and (23,24).

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A131574, A264498, A248712.

Select[Range[3000],PrimeNu[#]==PrimeOmega[#]==3&&FindInstance[x^2+y^2==#,{x,y},Integers]!={}&] (* Harvey P. Dale, Dec 16 2023 *)

cp's OEIS Frontend

A131574 Numbers n that are the product of two distinct odd primes and x^2 + y^2 = n has integer solutions.

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