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Search: id:A005579
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| A005579 |
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Least number of distinct prime factors in even numbers having an abundancy index > n.
(Formerly M0573)
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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The abundancy index of a number k is sigma(k)/k. - T. D. Noe (noe(AT)sspectra.com), May 08 2006
The first differences of this sequence, A005347, begin the same as the Fibonacci sequence A000045. - T. D. Noe (noe(AT)sspectra.com), May 08 2006
a(n+1)=smallest k such such that A005867(k+1)/A002110(k+1) > n+1. - Artur Jasinski (grafix(AT)csl.pl), Nov 06 2008
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REFERENCES
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R. Laatsch, Measuring the abundancy of integers. Math. Mag. 59 (1986), no. 2, 84-92.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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MATHEMATICA
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prod=1; k=0; Table[While[prod<=n, k++; prod=prod*Prime[k]/(Prime[k]-1)]; k, {n, 2, 25}] - T. D. Noe (noe(AT)sspectra.com), May 08 2006
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CROSSREFS
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Cf. A005580 (least number of distinct prime factors in odd numbers having an abundancy index > n).
A023199 (least k such that sigma(k)/k >= n) [From T. D. Noe (noe(AT)sspectra.com), Sep 18 2008]
Sequence in context: A058355 A099558 A018140 this_sequence A000381 A001115 A096824
Adjacent sequences: A005576 A005577 A005578 this_sequence A005580 A005581 A005582
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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EXTENSIONS
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Edited by T. D. Noe (noe(AT)sspectra.com), May 08 2006
a(26) added by T. D. Noe (noe(AT)sspectra.com), 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
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