

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
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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..13.
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: A135473 A242452 A190139 * A231222 A231436 A027932
Adjacent sequences: A005577 A005578 A005579 * A005581 A005582 A005583


KEYWORD

nonn,more,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Edited by T. D. Noe, May 08 2006


STATUS

approved



