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 A216896 #11 Sep 09 2019 11:57:17
%S A216896 38,133,172,253,460,477,580,612,717,996,1057,1568,1641,2244,2820,3193,
%T A216896 3253,3652,3848,4284,4733,4900,4908,5063,5380,6396,7220,8712,9245,
%U A216896 9972,10061,10181,10723,11316,11492,12488,12549,12567,13439,14063,14597,15660,15683
%N A216896 n - (sum of prime factors of n^2+1) is a positive square.
%H A216896 Amiram Eldar, <a href="/A216896/b216896.txt">Table of n, a(n) for n = 1..1000</a>
%e A216896 38 is in the sequence because the prime divisors of 38^2 + 1 = 1445 are {5, 17}, and 38 - (5+17) = 16 is square.
%p A216896 with(numtheory): for n from 1 to 2500 do:x:=n^2+1:y:=factorset(x):n1:=nops(y): s:=sum('y[i] ', 'i'=1..n1):z:=n-s:if n> s and sqrt(z)=floor(sqrt(z)) then printf(`%d, `, n): else fi:od:
%t A216896 aQ[n_] := (s = n - Plus @@ First @ Transpose @ FactorInteger[n^2+1]) > 0 && IntegerQ @ Sqrt @ s; Select[Range[16000], aQ] (* _Amiram Eldar_, Sep 09 2019 *)
%Y A216896 Cf. A193462.
%K A216896 nonn
%O A216896 1,1
%A A216896 _Michel Lagneau_, Sep 19 2012