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 A065656 #24 Dec 18 2024 22:29:34
%S A065656 1169,7777,41111,46097,668167,846817,2107519,3612769,17424241,
%T A065656 30666527,37526993,56323393,214746055,383523857,512376769,1021934641,
%U A065656 1228492849,1303949599,4056001351,7425397169,17073544447,17859428369,18452226887,46874737969,51411954391
%N A065656 Composite numbers k such that sigma(k)*phi(k) + 2*(k+1) is a square.
%C A065656 a(n) and square root of phi(a(n))*sigma(a(n)) + 2*a(n) + 2 are close to each other: e.g., a(7) = 2107519 and this square root is 2107458.
%C A065656 Since (p+1)*(p-1) + 2*(p+1) = p*p + 2*p + 1 = (p+1)^2 is a square, all primes are solutions.
%C A065656 73362272287 and 181264312447 are also terms. - _Donovan Johnson_, Jul 13 2012
%e A065656 k = 7777: sigma(7777) = 9792, phi(7777) = 6000 and 9792*6000 + 2*7778 = 587675556 = 7666^2.
%o A065656 (PARI) isok(k) = { !isprime(k) && issquare(sigma(k)*eulerphi(k) + 2*(k + 1)) } \\ _Harry J. Smith_, Oct 26 2009
%Y A065656 Cf. A062354, A000203, A000010, A065655.
%K A065656 nonn
%O A065656 1,1
%A A065656 _Labos Elemer_, Nov 12 2001
%E A065656 a(9)-a(15) from _Harry J. Smith_, Oct 26 2009
%E A065656 a(16)-a(20) from _Donovan Johnson_, May 24 2011
%E A065656 a(21)-a(25) from _Donovan Johnson_, Jul 13 2012