A074770 Numbers n such that tau(n) > tau(n+1), phi(n) > phi(n+1) and sigma(n) > sigma(n+1).

45, 117, 225, 273, 297, 345, 357, 405, 465, 513, 561, 621, 693, 705, 765, 777, 825, 837, 861, 885, 945, 1005, 1113, 1125, 1185, 1197, 1281, 1305, 1395, 1425, 1521, 1545, 1593, 1617, 1701, 1725, 1845, 1881, 1905, 1953, 1965, 2025, 2037, 2121, 2277

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Plot of a(n)/n for n = 1..360000

Formula

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

Example

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.

Maple

N:= 200: # to get the first N terms
prev:= [numtheory:-tau, numtheory:-phi, numtheory:-sigma](1):
count:= 0:
for n from 2 while count < N do
  tps:=  [numtheory:-tau, numtheory:-phi, numtheory:-sigma](n);
  if min(prev - tps) > 0 then count:= count+1; A[count]:= n-1 fi;
  prev:= tps;
od:
seq(A[i], i=1..N); # Robert Israel, Jan 09 2018

Mathematica

Select[Range[1, 3000], DivisorSigma[0, #] > DivisorSigma[0, #+1] && EulerPhi[#] > EulerPhi[#+1] && DivisorSigma[1, #] > DivisorSigma[1, #+1]&] (* Vaclav Kotesovec, Feb 16 2019 *)

Crossrefs

Sequence in context: A039528 A228058 A351533 * A348939 A370914 A343209

Adjacent sequences: A074767 A074768 A074769 * A074771 A074772 A074773

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved