A074770 - OEIS

%I #14 Feb 16 2019 03:13:04

%S 45,117,225,273,297,345,357,405,465,513,561,621,693,705,765,777,825,

%T 837,861,885,945,1005,1113,1125,1185,1197,1281,1305,1395,1425,1521,

%U 1545,1593,1617,1701,1725,1845,1881,1905,1953,1965,2025,2037,2121,2277

%N Numbers n such that tau(n) > tau(n+1), phi(n) > phi(n+1) and sigma(n) > sigma(n+1).

%H Robert Israel, <a href="/A074770/b074770.txt">Table of n, a(n) for n = 1..10000</a>

%H Vaclav Kotesovec, <a href="/A074770/a074770.jpg">Plot of a(n)/n for n = 1..360000</a>

%F It seems that a(n) is asymptotic to c*n with 52 < c < 54.

%e tau(117) = 6 > 4 = tau(118), phi(117) = 72 > 58 = phi(118), and sigma(117) = 182 > 180 = sigma(118); hence 117 is in the sequence.

%p N:= 200: # to get the first N terms

%p prev:= [numtheory:-tau,numtheory:-phi,numtheory:-sigma](1):

%p count:= 0:

%p for n from 2 while count < N do

%p   tps:=  [numtheory:-tau,numtheory:-phi,numtheory:-sigma](n);

%p   if min(prev - tps) > 0 then count:= count+1; A[count]:= n-1 fi;

%p   prev:= tps;

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Jan 09 2018

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

%K nonn

%O 1,1

%A _Benoit Cloitre_, Sep 07 2002