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Numbers k such that phi(k) + phi(k+1) divides sigma(k) + sigma(k+1).
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%I #22 Apr 25 2020 19:36:44

%S 1,5,52,55,185,506,551,590,644,667,707,2285,2587,2758,7551,10366,

%T 11336,11564,11798,12750,16616,16703,16764,17383,18239,24350,24415,

%U 26586,33263,35541,40382,63248,76247,76622,92379,95069,97341,106312,111388

%N Numbers k such that phi(k) + phi(k+1) divides sigma(k) + sigma(k+1).

%C Presumably the ratio (sigma(n)+sigma(n+1))/(phi(n)+phi(n+1)) can be arbitrarily large. - _Labos Elemer_, Sep 17 2004

%C The first term for which the ratio is k for k = 2, 3, ... is 1, 5, 644, 6513584, ... - _Amiram Eldar_, Mar 02 2020

%H Amiram Eldar, <a href="/A067282/b067282.txt">Table of n, a(n) for n = 1..200</a>

%t Select[Range[120000], Divisible[DivisorSigma[1, #] + DivisorSigma[1, # + 1], EulerPhi[#] + EulerPhi[# + 1]] &] (* _Amiram Eldar_, Mar 02 2020 *)

%t Select[Partition[Table[{n,EulerPhi[n],DivisorSigma[1,n]},{n,111400}],2,1], Divisible[ #[[1,3]]+#[[2,3]],#[[1,2]]+#[[2,2]]]&][[All,1,1]] (* _Harvey P. Dale_, Apr 25 2020 *)

%Y Cf. A000010, A000203, A092403, A092404.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Feb 23 2002

%E More terms from _Labos Elemer_, Sep 17 2004