A072370 - OEIS

%I #13 Sep 29 2019 03:10:56

%S 5,7,25,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,81,212,236,242,

%T 243,244,245,261,268,275,279,284,292,316,325,332,333,338,356,363,369,

%U 387,388,404,412,423,425,428,436,452,475,477,507,508,524,531,539,548

%N Numbers n such that tau(n) = log(n) + 2 * EulerGamma - 1 (rounded off), where tau(n) denotes the number of divisors of n and EulerGamma denotes the Euler-Mascheroni constant (0.5 is rounded to 0).

%C Dirichlet proved that the average value of tau(n) is approximately log(n) + 2 * EulerGamma - 1 (see the reference by Tattersall).

%D Tattersall, J. "Elementary Number Theory in Nine Chapters". Cambridge University Press, 1999.

%H Amiram Eldar, <a href="/A072370/b072370.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[10^3], DivisorSigma[0, # ] == Round[Log[ # ] + 2*EulerGamma - 1] &]

%Y Cf. A000005, A001620 (EulerGamma).

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jul 19 2002