A074771 Numbers k such that tau(k) < tau(k+1), phi(k) < phi(k+1) and sigma(k) < sigma(k+1).

62, 74, 134, 146, 254, 398, 404, 458, 482, 494, 554, 566, 614, 626, 662, 674, 692, 758, 764, 794, 818, 854, 914, 998, 1034, 1094, 1124, 1214, 1238, 1286, 1322, 1394, 1454, 1514, 1538, 1646, 1658, 1682, 1826, 1844, 1874, 1934, 2078, 2114, 2174, 2234, 2246

Offset: 1

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

Comments

There are few odd terms in the sequence, first one is 18015.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n)/n for n = 1..360000

Crossrefs

Subsequence of A074772 and A074775.

Cf. A000005, A000010, A000203.

Programs

Mathematica

Select[Range[1, 3000], DivisorSigma[0,#] < DivisorSigma[0,#+1] && EulerPhi[#] < EulerPhi[#+1] && DivisorSigma[1,#] < DivisorSigma[1,#+1]&] (* Vaclav Kotesovec, Feb 16 2019 *)
Position[Partition[Table[{DivisorSigma[0,n],EulerPhi[n],DivisorSigma[1,n]},{n,2300}],2,1],?(Max[#[[1]]-#[[2]]]<0&),1,Heads-> False]// Flatten (* _Harvey P. Dale, Jun 23 2019 *)

Formula

It seems that a(n) is asymptotic to c*n with 51<=c<=52