cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A074772 #18 Dec 11 2020 15:36:36
%S A074772 62,74,134,146,188,206,254,274,278,284,356,362,386,398,404,422,428,
%T A074772 454,458,482,494,538,554,566,614,626,662,674,692,746,758,764,794,818,
%U A074772 854,866,890,914,926,934,956,998,1004,1028,1034,1052,1070,1082,1084,1094
%N A074772 Numbers k such that tau(k) < tau(k+1) and phi(k) < phi(k+1).
%C A074772 There are few odd terms in the sequence, first one is 18015.
%H A074772 Amiram Eldar, <a href="/A074772/b074772.txt">Table of n, a(n) for n = 1..10000</a>
%H A074772 Vaclav Kotesovec, <a href="/A074772/a074772.jpg">Plot of a(n)/n for n = 1..1600000</a>
%F A074772 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]
%t A074772 Select[Range[1, 1000], DivisorSigma[0,#] < DivisorSigma[0,#+1] && EulerPhi[#] < EulerPhi[#+1]&] (* _Vaclav Kotesovec_, Feb 16 2019 *)
%t A074772 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 *)
%Y A074772 Subsequence of A074775.
%Y A074772 Cf. A000005, A000010.
%K A074772 nonn
%O A074772 1,1
%A A074772 _Benoit Cloitre_, Sep 07 2002