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 A386304 #11 Jul 23 2025 12:07:05
%S A386304 1,16,27,75,128,343,475,600,663,715,759,1015,1845,2679,3717,3933,4440,
%T A386304 5083,5325,5467,6120,6210,6325,6405,6859,7029,8349,8541,8664,9125,
%U A386304 9960,12045,12427,12535,13509,15067,16677,18693,18711,21783,22797,23250,23560,24605,25527,26496,26967,27117,28557
%N A386304 Numbers k such that k - A067666(k) is a square.
%C A386304 Numbers k such that k minus the sum of the squares of its prime factors with multiplicity is a square.
%C A386304 Is there any number other than 1 in both this sequence and A386257?
%C A386304 Contains no semiprimes.
%H A386304 Robert Israel, <a href="/A386304/b386304.txt">Table of n, a(n) for n = 1..10000</a>
%e A386304 a(4) = 75 is a term because 75 = 3 * 5^2 and 75 - 3^2 - 2 * 5^2 = 16 = 4^2 is a square.
%p A386304 filter:= proc(n) local t;
%p A386304 issqr(n - add(t[1]^2*t[2], t=ifactors(n)[2]))
%p A386304 end proc:
%p A386304 select(filter, [$1..10^5]);
%t A386304 spf[{p_,e_}]:=e*p^2;Q[k_]:=IntegerQ[Sqrt[k-Total[spf/@FactorInteger[k]]]];Select[Range[29000],Q[#]&] (* _James C. McMahon_, Jul 23 2025 *)
%o A386304 (PARI) isok(k) = my(f=factor(k)); issquare(k - sum(i=1, #f~, f[i, 1]^2*f[i, 2])); \\ _Michel Marcus_, Jul 20 2025
%Y A386304 Cf. A067666, A386257.
%K A386304 nonn
%O A386304 1,2
%A A386304 _Will Gosnell_ and _Robert Israel_, Jul 17 2025