

A087416


Take unbounded lunar divisors of n as defined in A087029, add them using lunar addition. See A087083 for their conventional sum.


3



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
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OFFSET

1,1


COMMENTS

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 : dn) == 2*n (both sum and * lunar)", no such numbers exist because 9n, 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 : dn, d != n) == n", no such numbers exist. For suppose n is perfect. n != 9 (since 9 is 9's only divisor). Then 9n and 9 != n, so sum (d : dn, 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 : dn, d!=n) is one digit shorter than n.


LINKS

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


CROSSREFS

Sequence in context: A106326 A245400 A088471 * A290546 A291720 A290832
Adjacent sequences: A087413 A087414 A087415 * A087417 A087418 A087419


KEYWORD

nonn,easy,base


AUTHOR

Marc LeBrun and N. J. A. Sloane, Oct 19 2003


EXTENSIONS

More terms from David Applegate, Nov 07 2003


STATUS

approved



