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A184977
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a(n) = Sum_{k=1..n} floor(k*gamma) where gamma is Euler's constant (A001620).
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1
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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
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OFFSET
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1,3
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COMMENTS
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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)
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..5000
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FORMULA
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Partial sums of A038128.
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MAPLE
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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:
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MATHEMATICA
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Table[Sum[Floor[k*EulerGamma], {k, 1, n}], {n, 50}] (* G. C. Greubel, Jun 02 2017 *)
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PROG
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(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
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CROSSREFS
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Cf. A001620, A038128.
Sequence in context: A194213 A194209 A183143 * A025705 A022792 A025697
Adjacent sequences: A184974 A184975 A184976 * A184978 A184979 A184980
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Mar 27 2011
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EXTENSIONS
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Name edited by Jon E. Schoenfield, Apr 02 2017
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STATUS
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approved
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