Suzanne Set

The $n$th Suzanne set $S_n$ is defined as the set of Composite Numbers $x$ for which $n\vert S(x)$ and $n\vert S_p(x)$, where

$$x=a_0+a_1(10^1)+\ldots+a_d(10^d)=p_1p_2\cdots p_n,$$

and

$$S(x) = \sum_{j=0}^d a_j$$

$$S_p(x) = \sum_{i=1}^m S(p_i).$$

Every Suzanne set has an infinite number of elements. The Suzanne set $S_n$ is a superset of the Monica Set $M_n$.

See also Monica Set

References

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