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

1,1

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

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]

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 *)

Crossrefs

Subsequence of A074775.

Cf. A000005, A000010.

Sequence in context: A294738 A044997 A138172 * A074771 A342258 A039391

Adjacent sequences: A074769 A074770 A074771 * A074773 A074774 A074775

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved