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Suzanne Set


The nth Suzanne set S_n is defined as the set of composite numbers x for which n|S(x) and n|S_p(x), where

x=a_0+a_1(10^1)+...+a_d(10^d)
(1)
=p_1p_2...p_m,
(2)

and

S(x)=sum_(j=0)^(d)a_j
(3)
S_p(x)=sum_(i=1)^(m)S(p_i).
(4)

Every Suzanne set has an infinite number of elements.

The following table gives the first few Suzanne numbers in S_n for small n.

nOEISS_n
1A0182521, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ...
2A1022164, 8, 15, 22, 26, 35, 42, 44, 60, 62, 64, ...
3A1022179, 24, 27, 42, 60, 72, 78, 81, 105, 114, ...

The Suzanne set S_n is a subset of the Monica set M_n.


See also

Monica Set

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References

Sloane, N. J. A. Sequences A018252, A102216, and A102217 in "The On-Line Encyclopedia of Integer Sequences."Smith, M. "Cousins of Smith Numbers: Monica and Suzanne Sets." Fib. Quart. 34, 102-104, 1996.

Referenced on Wolfram|Alpha

Suzanne Set

Cite this as:

Weisstein, Eric W. "Suzanne Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SuzanneSet.html

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