A306358 Odd numbers which are the sum of two squares in two or more different ways.

25, 65, 85, 125, 145, 169, 185, 205, 221, 225, 265, 289, 305, 325, 365, 377, 425, 445, 481, 485, 493, 505, 533, 545, 565, 585, 625, 629, 685, 689, 697, 725, 745, 765, 785, 793, 841, 845, 865, 901, 905, 925, 949, 965, 985, 1025, 1037, 1073, 1105, 1125, 1145, 1157, 1165, 1189, 1205, 1225, 1241

Offset: 1

Author

Joerg Arndt, Feb 10 2019

Keywords

• nonn

Comments

Odd terms of A118882.

Odd numbers k such that A000161(k) >= 2.

Examples

			The decompositions of the first terms are
25: [[4, 3], [5, 0]]
65: [[7, 4], [8, 1]]
85: [[7, 6], [9, 2]]
125: [[10, 5], [11, 2]]
145: [[9, 8], [12, 1]]
169: [[12, 5], [13, 0]]
185: [[11, 8], [13, 4]]
205: [[13, 6], [14, 3]]
221: [[11, 10], [14, 5]]
225: [[12, 9], [15, 0]]
265: [[12, 11], [16, 3]]
289: [[15, 8], [17, 0]]
305: [[16, 7], [17, 4]]
325: [[15, 10], [17, 6], [18, 1]]
365: [[14, 13], [19, 2]]
377: [[16, 11], [19, 4]]
		

Programs

PARI

A000161(n)=sum(k=sqrtint((n-1)\2)+1, sqrtint(n), issquare(n-k^2));
is(n)=if(n%2==1, A000161(n)>1, 0);
select(is,vector(1300,n,n))

Python

from itertools import count, islice
from math import prod
from sympy import factorint
def A306358_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue+1-(startvalue&1),1),2):
        f = factorint(n)
        if 1>1):
            yield n
A306358_list = list(islice(A306358_gen(),30)) # Chai Wah Wu, Sep 09 2022