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A189686
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Superabundant numbers (A004394) satisfying the reverse of Robin's inequality (A091901).
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4
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2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 2520, 5040
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OFFSET
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1,1
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COMMENTS
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5040 is the last element in the sequence if and only if the Riemann Hypothesis is true. (See Akbary and Friggstad in A004394.)
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LINKS
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G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, arXiv:1112.6010 [math.NT], 2011-2012; Ramanujan J., 29 (2012), 359-384.
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FORMULA
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MATHEMATICA
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kmax = 10^4;
A004394 = Join[{1}, Reap[For[r = 1; k = 2, k <= kmax, k = k + 2, s = DivisorSigma[-1, k]; If[s > r, r = s; Sow[k]]]][[2, 1]]];
A067698 = Select[Range[2, kmax], DivisorSigma[1, #] > Exp[EulerGamma] # Log[Log[#]]&];
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PROG
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(PARI) is(n)=sigma(n) >= exp(Euler) * n * log(log(n)); \\ A067698
lista(nn) = my(r=1, t); forstep(n=2, nn, 2, t=sigma(n, -1); if(t>r && is(n), r=t; print1(n, ", "))); \\ Michel Marcus, Jan 28 2019; adapted from A004394
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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