This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005580 M2740 #37 Jul 08 2025 16:31:54
%S A005580 0,1,3,8,21,54,141,372,995,2697,7397,20502,57347,161658,458788,
%T A005580 1309626,3757383,10828011,31326513,90945528
%N A005580 a(n) = smallest number k such that Product_{i=2..k+1} prime(i)/(prime(i)-1) > n.
%C A005580 Laatsch (1986) proved that a(n) gives the smallest number of distinct prime factors in odd numbers having an abundancy index > n.
%C A005580 The abundancy index of a number k is sigma(k)/k. - _T. D. Noe_, May 08 2006
%D A005580 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005580 R. K. Guy, <a href="/A000081/a000081.pdf">Letter to N. J. A. Sloane, 1988-04-12</a> (annotated scanned copy)
%H A005580 Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.
%F A005580 For n > 0, a(n) = A005579(2n)-1. - _T. D. Noe_, May 08 2006
%t A005580 prod=1; k=1; Table[While[prod<=n, k++; prod=prod*Prime[k]/(Prime[k]-1)]; k-1, {n,0,12}] (* _T. D. Noe_, May 08 2006 *)
%Y A005580 Cf. A005579.
%K A005580 nonn,more
%O A005580 0,3
%A A005580 _N. J. A. Sloane_
%E A005580 Edited by _T. D. Noe_, May 08 2006
%E A005580 a(14)-a(19) from the data at A005579 added by _Amiram Eldar_, Mar 21 2019
%E A005580 Edited and a(0)-a(1) prepended by _Max Alekseyev_, Jan 25 2025