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A005580 Least number of distinct prime factors in odd numbers having an abundancy index > n.
(Formerly M2740)
1

%I M2740 #19 Mar 21 2019 13:51:17

%S 3,8,21,54,141,372,995,2697,7397,20502,57347,161658,458788,1309626,

%T 3757383,10828011,31326513,90945528

%N Least number of distinct prime factors in odd numbers having an abundancy index > n.

%C The abundancy index of a number k is sigma(k)/k. - _T. D. Noe_, May 08 2006

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. K. Guy, <a href="/A000081/a000081.pdf">Letter to N. J. A. Sloane, 1988-04-12</a> (annotated scanned copy)

%H Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.

%F a(n) = A005579(2n)-1. - _T. D. Noe_, May 08 2006

%t prod=1; k=1; Table[While[prod<=n, k++; prod=prod*Prime[k]/(Prime[k]-1)]; k, {n,2,12}] (* _T. D. Noe_, May 08 2006 *)

%Y Cf. A005579 (least number of distinct prime factors in even numbers having an abundancy index > n).

%K nonn,more

%O 2,1

%A _N. J. A. Sloane_.

%E Edited by _T. D. Noe_, May 08 2006

%E a(14)-a(19) from the data at A005579 added by _Amiram Eldar_, Mar 21 2019

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Last modified May 2 04:48 EDT 2024. Contains 372178 sequences. (Running on oeis4.)