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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
(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
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REFERENCES
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R. Laatsch, Measuring the abundancy of integers. Math. Mag. 59 (1986), no. 2, 84-92.
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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).
Adjacent sequences: A005576 A005577 A005578 this_sequence A005580 A005581 A005582
Sequence in context: A058355 A099558 A018140 this_sequence A000381 A001115 A096824
A023199 (least k such that sigma(k)/k >= n) [From T. D. Noe (noe(AT)sspectra.com), Sep 18 2008]
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KEYWORD
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nonn,new
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AUTHOR
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njas, 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
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