A306014 Numbers k such that A055228(k)^2 - A055228(k) is a multiple of k, where A055228(k) is ceiling(sqrt(k!)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 16, 28, 29, 30, 42, 46, 50, 52, 99, 134, 148, 165, 205, 245, 249, 315, 390, 441, 461, 525, 560, 763, 962, 1596, 1666, 1716, 1847, 1854, 1860, 3515, 4501, 5179, 6850, 7345, 7867, 8940, 9491, 9523, 15688, 19988, 23574, 23956

Offset: 1

Author

Ivan Stoykov, Jun 17 2018

Keywords

• nonn

Examples

			For k=6, A055228(6) = ceiling(sqrt(6!)) = 27, and 27^2-27 = 702, which is a multiple of 6.
		

References

• Hazewinkel, Michiel, ed. (2001) [1994], Gamma Function, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..89 (all terms up to 10^6, n = 1..70 from Jon E. Schoenfield)

Crossrefs

Cf. A000188, A055228.

Programs

Mathematica

Select[Range[4600],Divisible[Ceiling[Sqrt[#!]]^2-Ceiling[Sqrt[#!]],#]&] (* Harvey P. Dale, Mar 02 2023 *)

PARI

default(realprecision,10^5); for(n=1,10^4, if( Mod( ceil(sqrt(n!)) - ceil(sqrt(n!))^2 , n) == 0, print1(n,", "))); \\ Joerg Arndt, Jun 17 2018

Extensions

Terms > 99 from Joerg Arndt, Jun 17 2018