This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371011 #10 Mar 08 2024 08:01:35
%S A371011 1,8,16,32,64,81,125,128,256,512,625,648,729,1000,1024,1296,2000,2048,
%T A371011 2197,2401,2592,3125,4000,4096,4913,5000,5184,5832,6561,8000,8192,
%U A371011 10000,10125,10368,11664,14641,15625,16000,16384,17576,19208,20000,20736,23328,24389,25000
%N A371011 Cubefull numbers that are the sum of 2 squares.
%C A371011 For each term k, let p^e be the highest power of a prime p that divides k. Then e >= 4 is even for p == 3 (mod 4), or e >= 3 otherwise.
%H A371011 Amiram Eldar, <a href="/A371011/b371011.txt">Table of n, a(n) for n = 1..10000</a>
%H A371011 Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.27745.48487">Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression</a>, ResearchGate, 2024.
%F A371011 The number of terms that do not exceed x is ~ c * x^(1/3)/sqrt(log(x)), where c = (6/Pi^2) * sqrt(3) * (1 + 1/(3*(2^(1/3)-1))) * B * Product_{primes p == 1 (mod 4)} (1 + 1/((p^(1/3)-1)*(p+1))) * Product_{primes p == 3 (mod 4)} (1 + p^(1/3)/(p*(p^(2/3)-1))), where B is the Landau-Ramanujan constant (A064533) (Jakimczuk, 2024, Theorem 4.5, p. 47).
%F A371011 Sum_{n>=1} 1/a(n) = (5/4) * Product_{primes p == 1 (mod 4)} (1 + 1/(p^2*(p-1))) * Product_{primes p == 3 (mod 4)} (1 + 1/(p^2*(p^2-1))) = 1.281719491797642498... .
%t A371011 Select[Range[25000], SquaresR[2, #] > 0 && (# == 1 || Min[FactorInteger[#][[;; , 2]]] > 2) &]
%o A371011 (PARI) is(n) = {my(f=factor(n)); for(i=1, #f~, if(f[i, 2] < 3 || (f[i, 2]%2 && f[i, 1]%4 == 3), return(0))); 1;}
%Y A371011 Intersection of A001481 and A036966.
%Y A371011 Subsequence of A371010.
%Y A371011 Cf. A020893, A064533.
%K A371011 nonn,easy
%O A371011 1,2
%A A371011 _Amiram Eldar_, Mar 08 2024