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Search: id:A087416
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| A087416 |
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Take unbounded dismal divisors of n as defined in A087029, add them using dismal addition. See A087083 for their conventional sum. |
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+0
2
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| 9, 9, 9, 9, 9, 9, 9, 9, 9, 99, 99, 19, 19, 19, 19, 19, 19, 19, 19, 99, 99, 99, 29, 29, 29, 29, 29, 29, 29, 99, 99, 99, 99, 39, 39, 39, 39, 39, 39, 99, 99, 99, 99, 99, 49, 49, 49, 49, 49, 99, 99, 99, 99, 99, 99, 59, 59, 59, 59, 99, 99, 99, 99, 99, 99, 99, 69, 69, 69
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Two comments from David Applegate on dismal perfect numbers, Nov 08 2003:
If we define a perfect number by "n is dismally perfect if sum(d : d|n) == 2*n (both sum and * dismal)", no such numbers exist because 9|n, so the dismal sum of divisors ends in 9, but 2*n ends in 2.
If we define a perfect number by "n is dismally perfect if dismal sum (d : d|n, d != n) == n", no such numbers exist. For suppose n is perfect. n != 9 (since 9 is 9's only divisor). Then 9|n and 9 != n, so sum (d : d|n, d!=n) ends in 9 and thus so does n. But 9ish numbers are not divisible by any single digit < 9. Thus n has no divisors of the same length as n, other than n itself. So sum (d : d|n, d!=n) is one digit shorter than n.
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LINKS
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D. Applegate, C program for dismal arithmetic and number theory
Index entries for sequences related to dismal arithmetic
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CROSSREFS
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Sequence in context: A066568 A106326 A088471 this_sequence A068395 A144586 A141557
Adjacent sequences: A087413 A087414 A087415 this_sequence A087417 A087418 A087419
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KEYWORD
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nonn,easy
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AUTHOR
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Marc LeBrun and N. J. A. Sloane (njas(AT)research.att.com), Oct 19 2003
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EXTENSIONS
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More terms from David Applegate (david(AT)research.att.com), Nov 07 2003
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