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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 (list; graph; refs; listen; history; text; internal format)
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 : 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.

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]

Index entries for sequences related to dismal (or lunar) arithmetic

CROSSREFS

Sequence in context: A106326 A245400 A088471 * A290546 A290832 A290624

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

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Last modified August 19 16:24 EDT 2017. Contains 290809 sequences.