OFFSET
2,1
COMMENTS
The abundancy index of a number k is sigma(k)/k. - T. D. Noe, May 08 2006
The first differences of this sequence, A005347, begin the same as the Fibonacci sequence A000045. - T. D. Noe, May 08 2006
For speed and accuracy, the second Mathematica program uses 30-digit real numbers and interval arithmetic.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, Letter to N. J. A. Sloane, 1988-04-12 (annotated scanned copy)
R. K. Guy and N. J. A. Sloane, Correspondence, 1988.
Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 84-92.
MATHEMATICA
prod=1; k=0; Table[While[prod<=n, k++; prod=prod*Prime[k]/(Prime[k]-1)]; k, {n, 2, 25}] (* T. D. Noe, May 08 2006 *)
prod=Interval[1]; k=0; Table[While[Max[prod]<=n, k++; p=Prime[k]; prod=N[prod*p/(p-1), 30]]; If[Min[prod]>n, k, "too few digits"], {n, 2, 38}]
PROG
(PARI) a(n)=my(s=1, k); forprime(p=2, , s*=p/(p-1); k++; if(s>n, return(k))) \\ Charles R Greathouse IV, Aug 20 2015
CROSSREFS
Cf. A005580 (least number of distinct prime factors in odd numbers having an abundancy index > n).
KEYWORD
nonn
AUTHOR
EXTENSIONS
STATUS
approved