A248712 Numbers k that are the product of four distinct primes such that x^2+y^2 = k has integer solutions.

2210, 3770, 4810, 4930, 5330, 6290, 6890, 6970, 7930, 9010, 9490, 10370, 10730, 11570, 11890, 12410, 12610, 12818, 13130, 14170, 14690, 15130, 15170, 15370, 16354, 16490, 17170, 17690, 17810, 18122, 18530, 19210, 19370, 19610, 20410, 21170, 21730, 22490

Offset

1,1

Comments

Union of 2*A264498 and A264499. - Ray Chandler, Dec 09 2019

Links

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

Example

2210 is in the sequence because 2210 = 2*5*13*17, and x^2+y^2=2210 has integer solutions (x,y) = (1,47), (19,43), (23,41) and (29,37).
32045 is in the sequence because x^2 + y^2 = 32045 = 5*13*17*29 has solutions (x,y) = (2,179), (19,178), (46,173), (67,166), (74,163), (86,157), (109,142) and (122,131).

Prog

(Python)
from math import isqrt
from sympy import primerange, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A248712(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*r))-c for a, k in h(2, integer_nthroot(x, 4)[0]+1, 1) for b, m in h(k+1, integer_nthroot(x//k, 3)[0]+1, a+1) for c, r in h(m+1, isqrt(x//(k*m))+1, b+1)))
    return bisection(f, n, n) # Chai Wah Wu, Dec 21 2025

Crossrefs

Cf. A248649, A264498, A264499.

Sequence in context: A216408 A043659 A178458 * A226562 A300166 A031772

Adjacent sequences: A248709 A248710 A248711 * A248713 A248714 A248715

Keyword

nonn

Author

Colin Barker, Oct 12 2014

Status

approved