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A087416
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Take unbounded lunar divisors of n as defined in A087029, add them using lunar addition. See A087083 for their conventional sum.
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3
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Two comments from David Applegate on lunar perfect numbers, Nov 08 2003:
If we define a perfect number by "n is lunarly perfect if sum(d : d|n) == 2*n (both sum and * lunar)", no such numbers exist because 9|n, so the lunar sum of divisors ends in 9, but 2*n ends in 2.
If we define a perfect number by "n is lunarly perfect if lunar 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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Table of n, a(n) for n=1..69.
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic
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CROSSREFS
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Sequence in context: A106326 A245400 A088471 * A290546 A291720 A290832
Adjacent sequences: A087413 A087414 A087415 * A087417 A087418 A087419
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KEYWORD
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nonn,easy,base
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AUTHOR
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Marc LeBrun and N. J. A. Sloane, Oct 19 2003
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EXTENSIONS
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More terms from David Applegate, Nov 07 2003
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STATUS
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approved
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