A279609 a(n) = floor(H(k) + exp(H(k))*log(H(k))) - sigma(k) where H(k) is the k-th harmonic number Sum_{j=1..k} 1/j and k is the n-th colossally abundant number A004490(n).

0, 0, 0, 2, 6, 34, 207, 492, 9051, 143828, 306310, 963859, 5155084, 81053635, 1334916490, 29106956400, 58655156200, 1817551636000, 56466287472000, 376943525488000, 1144451930851200, 41803526752345600

Offset

2,4

Comments

By a theorem of J. C. Lagarias, the Riemann hypothesis is equivalent to the proposition that this sequence never takes a negative value. In fact, by inspection it appears to be monotone increasing; this conjecture implies the Riemann hypothesis but is not in any obvious way implied by it. Stronger conjectures are easy to formulate--for example, if F(n) is the function defined by this sequence, then F(n)/2^n also appears to be monotone increasing.

Links

Table of n, a(n) for n=2..23.

J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, Am. Math. Monthly 109 (#6, 2002), 534-543.

Crossrefs

Cf. A004490, A057641.

Sequence in context: A362224 A233396 A003499 * A253778 A346189 A018953

Adjacent sequences: A279606 A279607 A279608 * A279610 A279611 A279612

Keyword

nonn

Author

Gene Ward Smith, Dec 15 2016

Status

approved