

A279609


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


0



0, 0, 0, 2, 6, 34, 207, 492, 9051, 143828, 306310, 963859, 5155084, 81053635, 1334916490, 29106956400, 58655156200, 1817551636000, 56466287472000, 376943525488000, 1144451930851200, 41803526752345600
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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 formulatefor example, if F(n) is the function defined by this sequence, then F(n)/2^n also appears to be monotone increasing.


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CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



