A057640 a(n) = floor(H(n) + exp(H(n))*log(H(n))), where H(n) = Sum_{k=1..n} 1/k.

1, 3, 5, 7, 10, 12, 15, 17, 20, 23, 25, 28, 31, 33, 36, 39, 41, 44, 47, 50, 53, 56, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 149, 152, 155, 158, 161

Offset: 1

Author

N. J. A. Sloane, Oct 12 2000

Keywords

• nonn
• nice
• easy

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• Masazumi Honda and Takuya Yoda, String theory, N = 4 SYM and Riemann hypothesis, arXiv:2203.17091 [hep-th], 2022.
• Jeffrey C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, Am. Math. Monthly 109 (#6, 2002), 534-543.
• OEIS Plot 2, A057640 vs A000203

Crossrefs

Cf. A000203, A001008, A002805, A057641.

Programs

Mathematica

hn[n_]:=Module[{h=HarmonicNumber[n]},Floor[h+Exp[h]Log[h]]]; Array[hn,60] (* Harvey P. Dale, Aug 02 2013 *)

PARI

first(n) = { my(h = 0, res = vector(n)); for(i = 1, n, print1(i", "); h+=1/i; res[i] = floor(h+exp(h)*log(h)) ); res } \\ David A. Corneth, Apr 28 2022