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

1,1

Comments

Odd terms of A118882.

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

Links

Table of n, a(n) for n=1..57.

Example

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]]

Prog

(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<int(not any(e&1 for e in f.values())) + (((m:=prod(1 if p==2 else (e+1 if p&3==1 else (e+1)&1) for p, e in f.items()))+((((~n & n-1).bit_length()&1)<<1)-1 if m&1 else 0))>>1):
            yield n
A306358_list = list(islice(A306358_gen(), 30)) # Chai Wah Wu, Sep 09 2022

Crossrefs

Sequence in context: A159008 A183373 A354381 * A120961 A285579 A050993

Adjacent sequences: A306355 A306356 A306357 * A306359 A306360 A306361

Keyword

nonn

Author

Joerg Arndt, Feb 10 2019

Status

approved