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 A380902 #24 Mar 25 2025 08:59:35
%S A380902 16,27,48,54,270,528,1755,7216,7830,11934,69168,81702,100368,264654,
%T A380902 340470,559899,1397808,1586340,1695195,3837510,3918420,8989110,
%U A380902 9815568,13010448,15812550,19468816,26302590,75872430,132825616,133529580,180280539,271165488
%N A380902 Integers k with at least 1 proper factorization for which the sum of the squares of the factors equals k.
%C A380902 It is conjectured that this sequence is infinite, that it does not contain any squarefree terms (A005117), and that with the exception of 16 (2^4) and 27 (3^3) it does not contain any squareful terms (A001694) or examples where the factors are all primes.
%C A380902 It is unknown whether this sequence contains any terms that produce more than one example (improbable if the exponential growth trend holds, but this is also unknown), or whether a more efficient generator algorithm (than the brute-force one given) exists or could be feasible.
%e A380902 a(1) = 16: 2 * 2 * 2 * 2 = 2^2 + 2^2 + 2^2 + 2^2 = 16.
%e A380902 a(2) = 27: 3 * 3 * 3 = 3^2 + 3^2 + 3^2 = 27.
%e A380902 a(3) = 48: 2 * 2 * 2 * 6 = 2^2 + 2^2 + 2^2 + 6^2 = 48.
%o A380902 (PARI) a380902_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, return(if(sum(i=1, #f, f[i]^2)==x, 1, 0))); my(d, c=0); fordiv(r, d, if(d==1 || d==x || (#f && d<f[#f]), next); listput(f, d); c+=a380902_count(x, f); listpop(f)); return(c)} \\ _Charles L. Hohn_, Mar 09 2025
%Y A380902 Subset of A380760.
%Y A380902 Cf. A001694, A005117, A162247, A190882.
%K A380902 nonn
%O A380902 1,1
%A A380902 _Charles L. Hohn_, Feb 07 2025