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 A068418 #20 May 13 2023 13:50:31
%S A068418 12,56,260,992,1320,1976,2156,2754,3696,5520,13800,16256,19872,22560,
%T A068418 23688,25232,41072,87000,89964,133984,145888,366720,785808,851760,
%U A068418 1100864,1235052,1270208,1439552,1470720,2129400,2237888,4729664
%N A068418 Composite numbers k such that k - phi(k) divides sigma(k) - k.
%C A068418 If 2^p - 1 is prime (a Mersenne prime) then k = 2^p*(2^p - 1) is in the sequence because 3*k - 2*phi(k) = sigma(k) (see Comments at A068414) so sigma(k) - k = 2*(k - phi(k)) hence k - phi(k) divides sigma(k) - k. - _Farideh Firoozbakht_, Dec 31 2005
%C A068418 Also if 3*2^m - 1 is a prime greater than 5 then k = 15*2^(m+1)*(3*2^m - 1) is in the sequence because 4*k - 3*phi(k) = 4*15*2^(m+1)*(3*2^m - 1) - 3*2^(m+3)*(3*2^m - 2) = 24*(3*2^m)*(2^(m+2) - 1) = sigma(15)*sigma(3*2^m - 1)*sigma(2^(m+1)) = sigma(15*(3*2^m - 1)*2^(m+1)) = sigma(k) hence sigma(k) - k = 3*(k - phi(k)) and k - phi(k) divides sigma(k) - k. - _Farideh Firoozbakht_, Dec 31 2005
%H A068418 Donovan Johnson, <a href="/A068418/b068418.txt">Table of n, a(n) for n = 1..68</a> (terms < 10^11)
%t A068418 Do[s=(DivisorSigma[1, n]-n)/(n-EulerPhi[n]); If[ !PrimeQ[n]&&IntegerQ[s], Print[n]], {n, 2, 10000000}]
%o A068418 (PARI) for(n=1,300000, if((sigma(n)-n)%(n-eulerphi(n))==isprime(n),print1(n,",")))
%Y A068418 A068414 is the subsequence telling when the quotient is 2.
%Y A068418 Cf. A068414, A051953, A000203, A000668.
%K A068418 easy,nonn
%O A068418 1,1
%A A068418 _Benoit Cloitre_, Mar 03 2002
%E A068418 More terms from _Labos Elemer_, Apr 02 2002