|
|
A232438
|
|
Squares or double-squares that are the sum of two distinct nonzero squares in exactly one way.
|
|
1
|
|
|
25, 50, 100, 169, 200, 225, 289, 338, 400, 450, 578, 676, 800, 841, 900, 1156, 1225, 1352, 1369, 1521, 1600, 1681, 1682, 1800, 2025, 2312, 2450, 2601, 2704, 2738, 2809, 3025, 3042, 3200, 3362, 3364, 3600, 3721, 4050, 4624, 4900, 5202, 5329, 5408, 5476
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Numbers with exactly one prime factor of form 4k+1 with multiplicity 2, and without prime factor of form 4k+3 to an odd multiplicity.
|
|
LINKS
|
|
|
FORMULA
|
Terms are obtained by the products A125853(k)*A002144(p)^2 for k, p > 0, ordered by increasing values.
|
|
EXAMPLE
|
25 = 5^2 = 16+9; 50 = 2*5^2 = 49+1.
|
|
MATHEMATICA
|
Select[Range[10^4], (IntegerQ[Sqrt[#]] || IntegerQ[Sqrt[#/2]]) && Count[ PowersRepresentations[#, 2, 2], {x_, y_} /; Unequal[0, x, y]] == 1 &]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|