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A306014 Numbers k such that A055228(k)^2 - A055228(k) is a multiple of k, where A055228(k) is ceiling(sqrt(k!)). 1

%I

%S 1,2,3,4,5,6,7,8,9,10,14,16,28,29,30,42,46,50,52,99,134,148,165,205,

%T 245,249,315,390,441,461,525,560,763,962,1596,1666,1716,1847,1854,

%U 1860,3515,4501,5179,6850,7345,7867,8940,9491,9523,15688,19988,23574,23956

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

%D 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

%H Chai Wah Wu, <a href="/A306014/b306014.txt">Table of n, a(n) for n = 1..89</a> (all terms up to 10^6, n = 1..70 from Jon E. Schoenfield)

%e For n=6, ceiling(sqrt(6!))=27, (ceiling(sqrt(6!))^2=729, and 729-27 = 702, which is a multiple of 6.

%o (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

%Y Cf. A000188, A055228.

%K nonn

%O 1,2

%A _Ivan Stoykov_, Jun 17 2018

%E Terms > 99 from _Joerg Arndt_, Jun 17 2018

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Last modified September 22 18:56 EDT 2021. Contains 347608 sequences. (Running on oeis4.)