A215000 a(n) = floor(exp(1 + 1/2 + 1/3 + ... + 1/n)).

2, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 95, 97, 98, 100, 102, 104, 105, 107, 109, 111, 113, 114

Offset: 1

Author

Clark Kimberling, Aug 18 2012

Keywords

• nonn

Comments

a(n) is the greatest integer k for which log k < 1 + 1/2 + ... + 1/n.

a(n) is asymptotically equals to n*e^(gamma) for large values of n where 'gamma' is the Euler-Mascheroni constant (Cf. A001620). - Balarka Sen, Aug 19 2012

Examples

			log 2 < 1 < log 3, so a(1) = 2;
log 4 < 1 + 1 + 1/2 < log 5, so a(2) = 4;
log 6 < 1 + 1/2 + 1/3 < log 7, so a(3) = 6.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A215001, A001620, A073004.

Programs

Magma

[Floor(Exp((&+[1/k :k in [1..n]]))): n in [1..30]]; // G. C. Greubel, Feb 01 2018

Mathematica

f[n_] := Sum[1/h, {h, n}]; Table[Floor[E^f[n]], {n, 100}]
Table[Floor[Exp[HarmonicNumber[n]]], {n, 1, 100}] (* G. C. Greubel, Aug 30 2018 *)

PARI

a(n) = floor(exp(sum(X=1,n,1/X))) \\ Balarka Sen, Aug 19 2012