A074772 Numbers k such that tau(k) < tau(k+1) and phi(k) < phi(k+1).

62, 74, 134, 146, 188, 206, 254, 274, 278, 284, 356, 362, 386, 398, 404, 422, 428, 454, 458, 482, 494, 538, 554, 566, 614, 626, 662, 674, 692, 746, 758, 764, 794, 818, 854, 866, 890, 914, 926, 934, 956, 998, 1004, 1028, 1034, 1052, 1070, 1082, 1084, 1094

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..1600000

Crossrefs

Subsequence of A074775.

Cf. A000005, A000010.

Programs

Mathematica

Select[Range[1, 1000], DivisorSigma[0,#] < DivisorSigma[0,#+1] && EulerPhi[#] < EulerPhi[#+1]&] (* Vaclav Kotesovec, Feb 16 2019 *)
Position[Partition[Table[{DivisorSigma[0,n],EulerPhi[n]},{n,1100}],2,1], ?(#[[1,1]]<#[[2,1]]&&#[[1,2]]<#[[2,2]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, Dec 11 2020 *)

Formula

It seems that a(n) is asymptotic to c*n with 14<=c<=16. [This conjecture is false, see plot. - Vaclav Kotesovec, Feb 16 2019]