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 A065655 #33 Dec 18 2024 22:41:37 %S A065655 28,90,156,184,374,1855,2162,2170,2280,2376,2415,2665,3160,4970,5270, %T A065655 5740,6402,6494,7414,8400,9118,10656,11155,12400,14632,14910,15010, %U A065655 15906,18183,18792,22648,24645,24734,24920,25844,26670,27478,28990 %N A065655 Composite numbers k such that sigma(k)*(phi(k) + 2) is a square. %H A065655 Amiram Eldar, <a href="/A065655/b065655.txt">Table of n, a(n) for n = 1..2500</a> (terms 1..500 from Harry J. Smith) %e A065655 Since for a prime p, sigma(p)*(phi(p) + 2) = (p+1)*((p-1) + 2) = (p+1)^2 is a square, all primes are solutions. %e A065655 For k = 28, sigma(28) = 56, phi(28) = 12, 56*(12 + 2) = 784 = 28*28, so 28 is a composite solution. %t A065655 Select[Range@ 30000, Function[n, And[CompositeQ@ n, IntegerQ@ Sqrt[# EulerPhi@ n + 2 #] &@ DivisorSigma[1, n]]]] (* _Michael De Vlieger_, Mar 18 2017 *) %o A065655 (PARI) is(k) = if(k == 1 || isprime(k), 0, my(f = factor(k), s = sigma(f), p = eulerphi(f)); issquare(s * (p+2))); \\ _Amiram Eldar_, Nov 12 2024 %Y A065655 Cf. A000010, A000203. %K A065655 nonn %O A065655 1,1 %A A065655 _Labos Elemer_, Nov 12 2001