A371013 Numbers that are the sum of 2 squares and divisible by the square of their largest prime factor.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Rafael Jakimczuk, Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression, ResearchGate, 2024.

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

Intersection of A001481 and A070003.

Sequence in context: A034038 A069265 A336359 * A359680 A003679 A079432

Adjacent sequences: A371010 A371011 A371012 * A371014 A371015 A371016

Keyword

nonn,easy

Author

Amiram Eldar, Mar 08 2024

Status

approved