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Search: id:A125639
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| A125639 |
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Doubly abundant numbers - numbers k such that k and s(k) are abundant. |
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+0
3
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| 24, 30, 42, 54, 60, 66, 78, 84, 90, 96, 102, 114, 120, 126, 132, 138, 140, 150, 168, 174, 176, 180, 186, 198, 204, 210, 216, 222, 224, 234, 240, 246, 252, 258, 264, 270, 276, 280, 282, 294, 306, 308, 312, 318, 330, 340, 342, 348, 354, 360, 364, 366, 378, 380
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OFFSET
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1,1
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COMMENT
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Unlike abundant numbers, not all multiples of doubly abundant numbers are doubly abundant; for instance, 48 is not doubly abundant. There are infinitely many doubly abundant numbers; for instance, all numbers of the form 24*25^k are doubly abundant. Such a number is abundant, being a multiple of an abundant number, and s(24*25^k) = s(24)*s(25^k) + 24*s(25^k) + 25^k*s(24), which is a multiple of s(24) = 36.
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EXAMPLE
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24 is doubly abundant because it is abundant (s(24) = 36) and s(24) is abundant (s(36) = 45).
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CROSSREFS
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Cf. A005101, A125640.
Adjacent sequences: A125636 A125637 A125638 this_sequence A125640 A125641 A125642
Sequence in context: A048945 A111398 A030626 this_sequence A076496 A125640 A141545
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KEYWORD
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nonn
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AUTHOR
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Gabriel Cunningham (gabriel.cunningham(AT)gmail.com), Nov 28 2006
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