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Conjectured lower bounds for the Riemann hypothesis function floor(H(k) + exp(H(k))*log(H(k))) - sigma(k).
2

%I #15 Nov 02 2024 04:08:03

%S 0,1,2,6,23,33,34,78,105,207,492,1536,1667,3036,5155,5206,7682,8748,

%T 9051,15895,21295,22160,36300,58331,58657,71186,81276,91902,126789,

%U 142721,143828,240466,291217,306310,471093,743434,872803,963860,1652806,1742555

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

%C 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,

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

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

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

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

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

%C The pattern continues.

%Y Cf. A057641, A176679.

%K nonn,changed

%O 1,3

%A _T. D. Noe_, Mar 28 2013