The th Monica set is defined as the set of composite numbers for which , where
(1)
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(2)
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and
(3)
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(4)
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Every Monica set has an infinite number of elements.
The Monica set is a superset of the Suzanne set .
The following table gives the first few Monica numbers in for small .
OEIS | ||
1 | A018252 | 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ... |
2 | A102218 | 4, 8, 10, 12, 14, 15, 22, 26, 27, 35, 42, 44, ... |
3 | A102219 | 9, 16, 24, 27, 28, 32, 40, 42, 49, 52, 56, 60, ... |
If is a Smith number, then it is a member of the Monica set for all . For any integer , if is a -Smith number, then .