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Using the lunar product (see A087062 for definition), numbers n such that if n divides a*b, then n must divide either a or b. The multiplicative identity, 9, is excluded by convention.
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%I #14 Aug 06 2014 16:19:01

%S 1,2,3,4,5,6,7,8,90

%N Using the lunar product (see A087062 for definition), numbers n such that if n divides a*b, then n must divide either a or b. The multiplicative identity, 9, is excluded by convention.

%C This condition is one of the definitions of a prime, so these numbers could be called lunar primes (cf. A087097).

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%e 90 is a member because the lunar multiples of 90 are the same as the numbers ending with a 0 and if neither a nor b ends in 0, then neither does a*b.

%Y Cf. A087062, A087097.

%K base,fini,full,nonn,less

%O 1,2

%A _David Wasserman_, Aug 11 2005