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 A291880 #30 Sep 21 2017 13:21:40 %S A291880 3,4,5,6,8,10,20,22,40,76,80,108,160,204,320,640,1072,1280,2560,4192, %T A291880 5120,10240,20480,40960,49344,81920,163840,327680,655360,1310720, %U A291880 2621440,4197376,5242880,10485760,20971520,41943040,83886080,167772160,268460032,335544320,671088640,1073790976,1342177280,2684354560,5368709120 %N A291880 Numbers n such that phi(n) - 1 | sigma(n). %C A291880 Numbers n such that A109606(n) | A000203(n). %C A291880 All numbers of the form 5*2^x, with x >= 0, are part of the sequence (A020714). %C A291880 Values of the ratio sigma(n)/(phi(n)-1) are 4, 7, 2, 12, 5, 6, 6, 4, 6, 4, 6, 8, 6, 8, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 4, 6, ... %C A291880 Sequence contains also terms of the form 2^(n-2)*(2^n+3) where 2^n+3 is a prime and n > 3, like 22, 76, 1072, 4192, 4197376, 268460032. See A057733 for primes of the form 2^n+3. - _Michel Marcus_, Sep 17 2017 %e A291880 sigma(1072) = 2108, phi(1072) = 528 and 2108/(528 - 1) = 4. %p A291880 with(numtheory): P:=proc(q) local n; for n from 3 to q do %p A291880 if type(sigma(n)/(phi(n)-1),integer) then print(n); fi; od; end: P(10^7); %t A291880 Select[Range[3, 10^6], Divisible[DivisorSigma[1, #], EulerPhi[#] - 1] &] (* _Michael De Vlieger_, Sep 06 2017 *) %o A291880 (PARI) isok(n) = denominator(sigma(n)/(eulerphi(n)-1)) == 1; \\ _Michel Marcus_, Sep 06 2017 %Y A291880 Cf. A000010, A000203, A020714, A056097, A057733, A109606. %K A291880 nonn %O A291880 1,1 %A A291880 _Paolo P. Lava_, Sep 05 2017 %E A291880 a(34)-a(41) from _Michel Marcus_, Sep 15 2017 %E A291880 a(42)-a(45) from _Michel Marcus_, Sep 21 2017