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 A005579 Least number of distinct prime factors in even numbers having an abundancy index > n. (Formerly M0573) 4
 2, 3, 4, 6, 9, 14, 22, 35, 55, 89, 142, 230, 373, 609, 996, 1637, 2698, 4461, 7398, 12301, 20503, 34253, 57348, 96198, 161659, 272124, 458789, 774616, 1309627, 2216968, 3757384, 6375166, 10828012, 18409028, 31326514, 53354259, 90945529, 155142139 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = smallest k such that A002110(k)/A005867(k) > n. - Artur Jasinski, Nov 06 2008 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; 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). Cf. A023199 (least k such that sigma(k)/k >= n) - T. D. Noe, Sep 18 2008 Sequence in context: A099558 A018140 A256969 * A000381 A350588 A001115 Adjacent sequences:  A005576 A005577 A005578 * A005580 A005581 A005582 KEYWORD nonn AUTHOR EXTENSIONS Edited by T. D. Noe, May 08 2006 a(26) added by T. D. Noe, Sep 18 2008 Typo corrected by Vincent E. Yu (yu.vincent.e(AT)gmail.com), Aug 14 2009 a(27)-a(36) from Vincent E. Yu (yu.vincent.e(AT)gmail.com), Aug 14 2009 Comment corrected by T. D. Noe, Apr 04 2010 a(37)-a(39) from T. D. Noe, Nov 16 2010 STATUS approved

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Last modified September 28 20:34 EDT 2022. Contains 357081 sequences. (Running on oeis4.)