A079526 a(n) = floor( exp(H_n)*log(H_n) ) - sigma(n).

-1, -2, -1, -2, 2, -2, 4, 0, 4, 2, 10, -3, 13, 6, 9, 4, 20, 2, 23, 4, 17, 16, 31, -3, 29, 21, 26, 13, 42, 3, 46, 18, 36, 32, 41, 1, 57, 38, 45, 14, 65, 14, 69, 32, 41, 51, 78, 5, 75, 42, 66, 43, 90, 27, 78, 33, 76, 70, 103, -2, 107, 76, 71, 51, 98, 41, 120, 65, 98, 53

Offset: 1

Author

N. J. A. Sloane, Jan 22 2003

Keywords

• sign

Comments

M. Kaneko has shown that the Riemann hypothesis is equivalent to the assertion that a(n) > 0 for n > 60.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.

Crossrefs

H_n = sum of harmonic series (see A002387), sigma(n) = A000203.

Cf. A057641, A058209, A079527.

Programs

Magma

[Floor(Exp(HarmonicNumber(n))*Log(HarmonicNumber(n))) - DivisorSigma(1,n): n in [1..80]]; // G. C. Greubel, Jan 15 2019

Mathematica

f[n_] := Floor[Exp[HarmonicNumber[n]]Log[HarmonicNumber[n]]] - DivisorSigma[1, n]; Array[f, 70] (* Robert G. Wilson v, Dec 17 2016 *)

PARI

{h(n) = sum(k=1, n, 1/k)};
vector(80, n, floor( exp(h(n))*log(h(n))) - sigma(n,1) ) \\ G. C. Greubel, Jan 15 2019

Sage

[floor(exp(harmonic_number(n))*log(harmonic_number(n))) - sigma(n,1) for n in (1..80)] # G. C. Greubel, Jan 15 2019