A222761 Conjectured lower bounds for the Riemann hypothesis function floor(H(k) + exp(H(k))*log(H(k))) - sigma(k).

0, 1, 2, 6, 23, 33, 34, 78, 105, 207, 492, 1536, 1667, 3036, 5155, 5206, 7682, 8748, 9051, 15895, 21295, 22160, 36300, 58331, 58657, 71186, 81276, 91902, 126789, 142721, 143828, 240466, 291217, 306310, 471093, 743434, 872803, 963860, 1652806, 1742555

Offset: 1

Author

T. D. Noe, Mar 28 2013

Keywords

• nonn

Comments

Here H(k) is the k-th harmonic number, Sum_{i=1..k} 1/i, and sigma(k) is the sum of the divisors of k. This sequence gives the conjectured values of A057641 that form a lower bound. For instance,

all numbers x <= 0 appear for n <= 12 = A176679(3);

all numbers x <= 1 appear for n <= 24 = A176679(4);

all numbers x <= 2 appear for n <= 60 = A176679(5);

all numbers x <= 6 appear for n <= 120 = A176679(6);

all numbers x <= 23 appear for n <= 180 = A176679(7).

The pattern continues.

Crossrefs

Cf. A057641, A176679.