A067282 Numbers k such that phi(k) + phi(k+1) divides sigma(k) + sigma(k+1).

1, 5, 52, 55, 185, 506, 551, 590, 644, 667, 707, 2285, 2587, 2758, 7551, 10366, 11336, 11564, 11798, 12750, 16616, 16703, 16764, 17383, 18239, 24350, 24415, 26586, 33263, 35541, 40382, 63248, 76247, 76622, 92379, 95069, 97341, 106312, 111388

Offset: 1

Author

Benoit Cloitre, Feb 23 2002

Keywords

• nonn

Comments

Presumably the ratio (sigma(n)+sigma(n+1))/(phi(n)+phi(n+1)) can be arbitrarily large. - Labos Elemer, Sep 17 2004

The first term for which the ratio is k for k = 2, 3, ... is 1, 5, 644, 6513584, ... - Amiram Eldar, Mar 02 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000010, A000203, A092403, A092404.

Programs

Mathematica

Select[Range[120000], Divisible[DivisorSigma[1, #] + DivisorSigma[1, # + 1], EulerPhi[#] + EulerPhi[# + 1]] &] (* Amiram Eldar, Mar 02 2020 *)
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 *)

Extensions

More terms from Labos Elemer, Sep 17 2004