A067038 a(n) = floor(n^m) where m = Sum_{k=1..n} (1/k).

1, 2, 7, 17, 39, 80, 155, 284, 500, 849, 1395, 2233, 3487, 5329, 7989, 11770, 17068, 24395, 34410, 47947, 66063, 90080, 121643, 162787, 216013, 284381, 371612, 482210, 621605, 796306, 1014096, 1284233, 1617696, 2027457, 2528789, 3139618

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..500

Formula

a(n) = floor(n^H(n)), H = A001008/A002805. - Alois P. Heinz, Dec 03 2019

Example

a(4) = 17 as 1 + 1/2 + 1/3 + 1/4 = 2.08333333333333... and 4^2.08333333333333... = 17.9593927729499677029365287948669...;
a(11) = 1395 as 1 + 1/2 + ... + 1/10 + 1/11 = 3.01987734487... and 11^3.01987734487734487734487734487734 = 1395.9767238344363983227863965103...

Prog

(PARI) { m=0; for (n=1, 500, m+=1/n; write("b067038.txt", n, " ", floor(n^m)) ) } \\ Harry J. Smith, Apr 29 2010

Crossrefs

Cf. A001008, A002805.

Sequence in context: A009302 A154117 A173769 * A209398 A364756 A175660

Adjacent sequences: A067035 A067036 A067037 * A067039 A067040 A067041

Keyword

nonn

Author

Amarnath Murthy, Dec 29 2001

Extensions

Terms added by Harry J. Smith, Apr 29 2010

Status

approved