|
|
A371013
|
|
Numbers that are the sum of 2 squares and divisible by the square of their largest prime factor.
|
|
1
|
|
|
4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 125, 128, 144, 162, 169, 196, 200, 225, 242, 245, 250, 256, 288, 289, 324, 338, 361, 392, 400, 441, 450, 484, 490, 500, 512, 529, 576, 578, 605, 625, 648, 676, 722, 729, 784, 800, 841, 845, 882, 900, 961, 968, 980, 1000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The asymptotic density of this sequence within A001481 is zero. More precisely, the number of terms that do not exceed x is ~ o(x/sqrt(log(x))) (Jakimczuk, 2024, Theorem 4.10, p. 55).
|
|
LINKS
|
|
|
MATHEMATICA
|
Select[Range[1500], SquaresR[2, #] > 0 && FactorInteger[#][[-1 , 2]] > 1 &]
|
|
PROG
|
(PARI) is(n) = {my(f=factor(n)); if(n == 1 || f[#f~, 2] == 1, return(0)); for(i=1, #f~, if(f[i, 2]%2 && f[i, 1]%4 == 3, return(0))); 1; }
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|