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

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

1,1

Comments

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

Links

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

Example

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).

Mathematica

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

Prog

(Python)
from math import isqrt
from sympy import primerange, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A248649(n):
    def g(x): return sum(1 for p in primerange(x+1) if p&3!=3)
    def h(x, y, i): return enumerate((p for p in primerange(x, y) if p&3!=3), i)
    def f(x): return int(n+x-sum(g(x//(k*m))-b for a, k in h(2, integer_nthroot(x, 3)[0]+1, 1) for b, m in h(k+1, isqrt(x//k)+1, a+1)))
    return bisection(f, n, n) # Chai Wah Wu, Dec 20 2025

Crossrefs

Cf. A131574, A264498, A248712.

Sequence in context: A252362 A331629 A248943 * A050238 A115937 A365833

Adjacent sequences: A248646 A248647 A248648 * A248650 A248651 A248652

Keyword

nonn

Author

Colin Barker, Oct 12 2014

Status

approved