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

1,3

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

Formula

Partial sums of A038128.

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 *)

Prog

(PARI) a(n) = sum(k=1, n, floor(k*Euler)); \\ Michel Marcus, Apr 02 2017
(Magma) R:=RealField(100); [(&+[Floor(k*EulerGamma(R)): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Aug 27 2018

Crossrefs

Cf. A001620, A038128.

Sequence in context: A194213 A194209 A183143 * A025705 A022792 A025697

Adjacent sequences: A184974 A184975 A184976 * A184978 A184979 A184980

Keyword

nonn

Author

Michel Lagneau, Mar 27 2011

Extensions

Name edited by Jon E. Schoenfield, Apr 02 2017

Status

approved