A184977 a(n) = Sum_{k=1..n} floor(k*gamma) where gamma is Euler's constant (A001620).

0, 1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 39, 46, 54, 62, 71, 80, 90, 100, 111, 123, 135, 148, 161, 175, 190, 205, 221, 237, 254, 271, 289, 308, 327, 347, 367, 388, 409, 431, 454, 477, 501, 525, 550, 575, 601, 628, 655, 683, 711, 740, 770, 800, 831, 862, 894, 926, 959, 993, 1027, 1062

Offset: 1

Author

Michel Lagneau, Mar 27 2011

Keywords

• nonn
• changed

Comments

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.

gamma = 0.57721566490153286060651209... (A002852)

1/sqrt(3) = 0.577350269189625764509148... (A020760)

Starts to differ from A183143 at a(97). - R. J. Mathar, Aug 28 2025

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001620, A038128.

Programs

Magma

R:=RealField(100); [(&+[Floor(k*EulerGamma(R)): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Aug 27 2018

Maple

with(numtheory):Digits:=500:s:=0:c:=evalf(gamma(0)):for n from 1 to 100 do:
  s:=s+floor(n*c):printf(`%d, `,s):od:

Mathematica

Table[Sum[Floor[k*EulerGamma], {k, 1, n}], {n, 50}] (* G. C. Greubel, Jun 02 2017 *)

PARI

a(n) = sum(k=1, n, floor(k*Euler)); \\ Michel Marcus, Apr 02 2017

Formula

Partial sums of A038128.

Extensions

Name edited by Jon E. Schoenfield, Apr 02 2017