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 A203966 #45 Jan 09 2024 11:40:48 %S A203966 1,2,3,15,255,65535,83623935,4294967295,6992962672132095 %N A203966 Numbers n such that phi(n) divides n+1, where phi is Euler's totient function (A000010). %C A203966 Numbers k such that A060473(k) = 1. - _Robert G. Wilson v_, Jul 06 2014 %C A203966 Except for a(2), all terms are odd. - _Chai Wah Wu_, Jun 06 2017 %C A203966 Since gcd(phi(n),n) = 1, all terms are squarefree. Then, for n = p1 * ... * pk with primes p1 < ... < pk, (n+1)/phi(n) is very close to p1/(p1-1)*...*pk/(p1-1). Since p/(p-1) is decreasing as p grows, having (n+1)/phi(n) = 3 implies that p1 >= 5 and further that n >= 2.4*10^56 is a product of at least 33 primes. Similarly, having (n+1)/phi(n) >= 4 implies that n >= 1.6*10^30 is a product of at least 21 primes. Hence, the terms of this sequence below 1.6*10^30 have (n+1)/phi(n) = 2 and thus coincide with A050474. - _Max Alekseyev_, Jan 30 2022 %H A203966 D. H. Lehmer, <a href="http://dx.doi.org/10.1090/s0002-9904-1932-05521-5">On Euler's totient function</a>, Bulletin of the American Mathematical Society, 38 (1932), 745-751. %e A203966 15 is in the sequence because phi(15) = 8, and 8 divides 16 = 15 + 1 evenly. %t A203966 Select[Range[100000], Divisible[#+1, EulerPhi[#]]&] %Y A203966 Cf. A060473, A000010, A202855. %Y A203966 Superset of A050474. %K A203966 nonn,more %O A203966 1,2 %A A203966 _José María Grau Ribas_, Jan 08 2012 %E A203966 a(8) from _Donovan Johnson_, Jan 13 2012 %E A203966 a(9) confirmed by _Max Alekseyev_, Jan 30 2022