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

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

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, 1988-04-12 (annotated scanned copy)

Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 84-92.

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