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 A011251 #51 Dec 16 2021 22:37:56
%S A011251 312,560,588,1400,85632,147492,556160,569328,1590816,2013216,3343776,
%T A011251 4695456,9745728,12558912,22013952,23336172,30002960,52021242,
%U A011251 75007400,137617728,153587720,699117024,904683264,2468053248,2834395104,21669802880,48444151296
%N A011251 Numbers n such that phi(n) + sigma(n) = 3n.
%C A011251 n is necessarily composite.
%C A011251 From the Math. Rev.: if both q=7*2^{r-2}+2^s-1 and p=49*2^{2r-s-4}+7*2^{r-2}-5*2^{r-s-2}-1 are prime for 1 <= s < r-2, then n=2^r*3*p*q is a solution to the equation phi(n)+sigma(n)=3n . [R. K. Guy]
%C A011251 If 7*2^n-1 is prime then m = 2^(n+2)*3*(7*2^n-1) is in the sequence. Because phi(m) = 2^(n+2)*(7*2^n-2); sigma(m) = 7*2^(n+2)*(2^(n+3)-1) so phi(m)+sigma(m) = 2^(n+2)*((7*2^n-2)+(7*2^(n+3)-7)) = 2^(n+2)*(63*2^n-9) = 3*(2^(n+2)*3*(7*2^n-1)) = 3*m. Hence A112729 = 2^(A001771+2)*3*(7*2^A001771-1) is a subsequence of this sequence. - _Farideh Firoozbakht_, Dec 01 2005
%C A011251 If both numbers p=7*2^n+2^k-1 & q=49*2^(2n-k)+2^(n-k)*(7*2^k-5)-1 are prime and m=2^(n+2)*3*p*q then phi(m)+sigma(m)=3*m. Namely m is in the sequence. - _Farideh Firoozbakht_, Jan 11 2007
%D A011251 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. See Section B42, p. 151.
%D A011251 David Wells, Prime Numbers: The Most Mysterious Figures in Math, Hoboken, New Jersey, John Wiley & Sons (2005), 75.
%D A011251 Ming Zhi ZHANG, A note on the equation phi(n)+sigma(n)=3n, Sichuan Daxue Xuebao 37 (2000), no. 1, 39-40; MR1755990 (2001a:11009).
%H A011251 Donovan Johnson, <a href="/A011251/b011251.txt">Table of n, a(n) for n = 1..35</a> (terms < 5*10^12)
%H A011251 F. Firoozbakht, M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1.
%H A011251 Richard K. Guy, <a href="http://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360.
%H A011251 Kelley Harris, <a href="http://dx.doi.org/10.1016/j.jnt.2009.02.003">On the classification of integers n that divide phi(n)+sigma(n)</a>, J. Num. Theory 129 (2009) 2093-2110.
%t A011251 Reap[ Do[ If[ EulerPhi[n] + DivisorSigma[1, n] == 3 n, Print[n]; Sow[n]], {n, 0, 10^8, 2}]][[2, 1]] (* _Jean-François Alcover_, Feb 16 2012 *)
%o A011251 (PARI) is(n)=eulerphi(n)+sigma(n)==3*n \\ _Charles R Greathouse IV_, Nov 27 2013
%Y A011251 Cf. A001771, A112729, A011254, A011774, A015704.
%K A011251 nonn,nice
%O A011251 1,1
%A A011251 _N. J. A. Sloane_
%E A011251 More terms from _Jud McCranie_
%E A011251 a(26)-a(27) from _Donovan Johnson_, Feb 28 2012