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 A033631 #41 Sep 08 2022 08:44:51
%S A033631 1,87,362,1257,1798,5002,9374,21982,22436,25978,35306,38372,41559,
%T A033631 50398,51706,53098,53314,56679,65307,68037,89067,108946,116619,124677,
%U A033631 131882,136551,136762,138975,144014,160629,165554,170037,186231,192394,197806
%N A033631 Numbers k such that sigma(phi(k)) = sigma(k) where sigma is the sum of divisors function A000203 and phi is the Euler totient function A000010.
%C A033631 For corresponding values of phi(k) and sigma(k), see A115619 and A115620.
%C A033631 This sequence is infinite because for each positive integer k, 3^k*7*1979 and 3^k*7*2699 are in the sequence (the proof is easy). A108510 gives primes p like 1979 and 2699 such that for each positive integer k, 3^k*7*p is in this sequence. - _Farideh Firoozbakht_, Jun 07 2005
%C A033631 There is another class of [conjecturally] infinite subsets connected to A005385 (safe primes). Examples: Let s,t be safe primes, s<>t, then 3^2*5*251*s, 2^2*61*71*s, 2*61*s*t and 2*19*311*s are in this sequence. So is 3*s*A108510(m). (There are some obvious exceptions for small s, t.) - _Vim Wenders_, Dec 27 2006
%D A033631 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 87, p. 29, Ellipses, Paris 2008.
%D A033631 R. K. Guy, Unsolved Problems in Number Theory, B42.
%D A033631 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books 1997.
%D A033631 David Wells, Curious and Interesting Numbers (Revised), Penguin Books, page 114.
%H A033631 T. D. Noe, <a href="/A033631/b033631.txt">Table of n, a(n) for n = 1..1000</a>
%H A033631 J.-M. De Koninck, F. Luca, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/DeKoninck/dekoninck47.html">Positive integers n such that sigma(phi(n))=sigma(n)</a>, JIS 11 (2008) 08.1.5.
%H A033631 S. W. Golomb, <a href="/A006872/a006872_1.pdf">Equality among number-theoretic functions</a>, Unpublished manuscript. (Annotated scanned copy)
%t A033631 Do[If[DivisorSigma[1, EulerPhi[n]]==DivisorSigma[1, n], Print[n]], {n, 1, 10^5}]
%o A033631 (PARI) is(n)=sigma(eulerphi(n))==sigma(n) \\ _Charles R Greathouse IV_, Feb 13 2013
%o A033631 (Magma) [k:k in [1..200000]| DivisorSigma(1,EulerPhi(k)) eq DivisorSigma(1,k)]; // _Marius A. Burtea_, Feb 09 2020
%Y A033631 Cf. A000203, A000010, A006872, A115619, A115620.
%K A033631 nonn
%O A033631 1,2
%A A033631 _Jud McCranie_
%E A033631 Entry revised by _N. J. A. Sloane_, Apr 10 2006