

A005580


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


1



3, 8, 21, 54, 141, 372, 995, 2697, 7397, 20502, 57347, 161658, 458788, 1309626, 3757383, 10828011, 31326513, 90945528
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OFFSET

2,1


COMMENTS

The abundancy index of a number k is sigma(k)/k.  T. D. Noe, May 08 2006


REFERENCES

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


LINKS

Table of n, a(n) for n=2..19.
R. K. Guy, Letter to N. J. A. Sloane, 19880412 (annotated scanned copy)
Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 8492.


FORMULA

a(n) = A005579(2n)1.  T. D. Noe, May 08 2006


MATHEMATICA

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 *)


CROSSREFS

Cf. A005579 (least number of distinct prime factors in even numbers having an abundancy index > n).
Sequence in context: A242452 A190139 A335807 * A292619 A231222 A231436
Adjacent sequences: A005577 A005578 A005579 * A005581 A005582 A005583


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Edited by T. D. Noe, May 08 2006
a(14)a(19) from the data at A005579 added by Amiram Eldar, Mar 21 2019


STATUS

approved



