cp's OEIS Frontend

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

%I A306358 #11 Sep 10 2022 02:22:04
%S A306358 25,65,85,125,145,169,185,205,221,225,265,289,305,325,365,377,425,445,
%T A306358 481,485,493,505,533,545,565,585,625,629,685,689,697,725,745,765,785,
%U A306358 793,841,845,865,901,905,925,949,965,985,1025,1037,1073,1105,1125,1145,1157,1165,1189,1205,1225,1241
%N A306358 Odd numbers which are the sum of two squares in two or more different ways.
%C A306358 Odd terms of A118882.
%C A306358 Odd numbers k such that A000161(k) >= 2.
%e A306358 The decompositions of the first terms are
%e A306358 25: [[4, 3], [5, 0]]
%e A306358 65: [[7, 4], [8, 1]]
%e A306358 85: [[7, 6], [9, 2]]
%e A306358 125: [[10, 5], [11, 2]]
%e A306358 145: [[9, 8], [12, 1]]
%e A306358 169: [[12, 5], [13, 0]]
%e A306358 185: [[11, 8], [13, 4]]
%e A306358 205: [[13, 6], [14, 3]]
%e A306358 221: [[11, 10], [14, 5]]
%e A306358 225: [[12, 9], [15, 0]]
%e A306358 265: [[12, 11], [16, 3]]
%e A306358 289: [[15, 8], [17, 0]]
%e A306358 305: [[16, 7], [17, 4]]
%e A306358 325: [[15, 10], [17, 6], [18, 1]]
%e A306358 365: [[14, 13], [19, 2]]
%e A306358 377: [[16, 11], [19, 4]]
%o A306358 (PARI) A000161(n)=sum(k=sqrtint((n-1)\2)+1, sqrtint(n), issquare(n-k^2));
%o A306358 is(n)=if(n%2==1, A000161(n)>1, 0);
%o A306358 select(is,vector(1300,n,n))
%o A306358 (Python)
%o A306358 from itertools import count, islice
%o A306358 from math import prod
%o A306358 from sympy import factorint
%o A306358 def A306358_gen(startvalue=1): # generator of terms >= startvalue
%o A306358     for n in count(max(startvalue+1-(startvalue&1),1),2):
%o A306358         f = factorint(n)
%o A306358         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):
%o A306358             yield n
%o A306358 A306358_list = list(islice(A306358_gen(),30)) # _Chai Wah Wu_, Sep 09 2022
%K A306358 nonn
%O A306358 1,1
%A A306358 _Joerg Arndt_, Feb 10 2019