A074771 - OEIS

%I #18 Sep 12 2020 03:24:58

%S 62,74,134,146,254,398,404,458,482,494,554,566,614,626,662,674,692,

%T 758,764,794,818,854,914,998,1034,1094,1124,1214,1238,1286,1322,1394,

%U 1454,1514,1538,1646,1658,1682,1826,1844,1874,1934,2078,2114,2174,2234,2246

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

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

%H Amiram Eldar, <a href="/A074771/b074771.txt">Table of n, a(n) for n = 1..10000</a>

%H Vaclav Kotesovec, <a href="/A074771/a074771.jpg">Plot of a(n)/n for n = 1..360000</a>

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

%t Select[Range[1, 3000], DivisorSigma[0,#] < DivisorSigma[0,#+1] && EulerPhi[#] < EulerPhi[#+1] && DivisorSigma[1,#] < DivisorSigma[1,#+1]&] (* _Vaclav Kotesovec_, Feb 16 2019 *)

%t 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 *)

%Y Subsequence of A074772 and A074775.

%Y Cf. A000005, A000010, A000203.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Sep 07 2002