Pseudosmarandache Function

The pseudosmarandache function $Z(n)$ is the smallest integer such that

$$\sum_{k=1}^{Z(n)} k={\textstyle{1\over 2}}Z(n)[Z(n)+1]$$

is divisible by $n$. The values for $n=1$, 2, ... are 1, 3, 2, 7, 4, 3, 6, 15, 8, 4, ... (Sloane's A011772).

See also Smarandache Function

References

Ashbacher, C. ``Problem 514.'' Pentagon 57, 36, 1997.

Kashihara, K. ``Comments and Topics on Smarandache Notions and Problems.'' Vail: Erhus University Press, 1996.

Sloane, N. J. A. Sequence A011772 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.