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Monica Set

The $n$th Monica set $M_n$ is defined as the set of Composite Numbers $x$ for which $n\vert S(x)-S_p(x)$, where

x=a_0+a_1(10^1)+\ldots+a_d(10^d)=p_1p_2\cdots p_n,
\end{displaymath} (1)

$\displaystyle S(x)$ $\textstyle =$ $\displaystyle \sum_{j=0}^d a_j$ (2)
$\displaystyle S_p(x)$ $\textstyle =$ $\displaystyle \sum_{i=1}^m S(p_i).$ (3)

Every Monica set has an infinite number of elements. The Monica set $M_n$ is a subset of the Suzanne Set $S_n$. If $x$ is a Smith Number, then it is a member of the Monica set $M_n$ for all $n\in\Bbb{N}$. For any Integer $k>1$, if $x$ is a $k$-Smith Number, then $x\in M_{k-1}$.

See also Suzanne Set


Smith, M. ``Cousins of Smith Numbers: Monica and Suzanne Sets.'' Fib. Quart. 34, 102-104, 1996.

© 1996-9 Eric W. Weisstein