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%I #21 Sep 08 2022 08:45:55
%S 0,1,2,4,6,9,13,17,22,27,33,39,46,54,62,71,80,90,100,111,123,135,148,
%T 161,175,190,205,221,237,254,271,289,308,327,347,367,388,409,431,454,
%U 477,501,525,550,575,601,628,655,683,711,740,770,800,831,862,894,926,959,993,1027,1062
%N a(n) = Sum_{k=1..n} floor(k*gamma) where gamma is Euler's constant (A001620).
%C a(n) = A183143(n) for n = 1..96 where A183143(n) is the sequence floor(1/r) + floor(2/r) + ... + floor(n/r) and r = sqrt(3). It is interesting to note that a(n)/n^2 converges to gamma/2.
%C gamma = 0.57721566490153286060651209... (A002852)
%C 1/sqrt(3) = 0.577350269189625764509148... (A020760)
%H G. C. Greubel, <a href="/A184977/b184977.txt">Table of n, a(n) for n = 1..5000</a>
%F Partial sums of A038128.
%p with(numtheory):Digits:=500:s:=0:c:=evalf(gamma(0)):for n from 1 to 100 do:
%p s:=s+floor(n*c):printf(`%d, `,s):od:
%t Table[Sum[Floor[k*EulerGamma], {k, 1, n}], {n, 50}] (* _G. C. Greubel_, Jun 02 2017 *)
%o (PARI) a(n) = sum(k=1, n, floor(k*Euler)); \\ _Michel Marcus_, Apr 02 2017
%o (Magma) R:=RealField(100); [(&+[Floor(k*EulerGamma(R)): k in [1..n]]): n in [1..50]]; // _G. C. Greubel_, Aug 27 2018
%Y Cf. A001620, A038128.
%K nonn
%O 1,3
%A _Michel Lagneau_, Mar 27 2011
%E Name edited by _Jon E. Schoenfield_, Apr 02 2017