cp's OEIS Frontend

A108861 Numbers k that divide the sum of the digits of 2^k * k!.

%I A108861 #37 Jul 11 2023 15:13:57
%S A108861 1,2,3,5,6,9,27,81,126,159,205,252,254,267,285,675,1053,1086,1125,
%T A108861 1146,2007,5088,5382,5448,14652,23401,23574,24009,41004,66789,67482,
%U A108861 111480,866538,1447875,2413152,2414019,2417828,2421360,4045482,6713982
%N A108861 Numbers k that divide the sum of the digits of 2^k * k!.
%C A108861 Next term after 5448 is greater than 10000.
%C A108861 a(34) > 10^6. - _D. S. McNeil_, Mar 03 2009
%C A108861 a(39) > 2.54 * 10^6, if it exists. - _Kevin P. Thompson_, Oct 20 2021
%C A108861 a(41) > 7*10^6, if it exists. - _Kevin P. Thompson_, Dec 08 2021
%e A108861 9 is a term because the sum of the digits of 2^9 * 9! = 185794560 is 45 which is divisible by 9.
%t A108861 Do[If[Mod[Plus @@ IntegerDigits[2^n * n! ], n] == 0, Print[n]], {n, 1, 10000}]
%t A108861 Select[Range[6714000],Mod[Total[IntegerDigits[2^# #!]],#]==0&] (* _Harvey P. Dale_, Jul 11 2023 *)
%o A108861 (PARI) isok(k) = !(sumdigits(2^k * k!) % k); \\ _Michel Marcus_, Oct 20 2021
%o A108861 (Python)
%o A108861 from itertools import islice
%o A108861 def A108861(): # generator of terms
%o A108861     k, k2, kf = 1, 2, 1
%o A108861     while True:
%o A108861         c = sum(int(d) for d in str(k2*kf))
%o A108861         if not c % k: yield k
%o A108861         k += 1
%o A108861         k2 *= 2
%o A108861         kf *= k
%o A108861 A108861_list = list(islice(A108861(),10)) # _Chai Wah Wu_, Oct 26 2021
%Y A108861 Cf. A000165, A007953, A052582.
%K A108861 nonn,base,hard,more
%O A108861 1,2
%A A108861 _Ryan Propper_, Jul 11 2005
%E A108861 a(25)-a(33) from _D. S. McNeil_, Mar 03 2009
%E A108861 a(34)-a(38) from _Kevin P. Thompson_, Oct 20 2021
%E A108861 a(39)-a(40) from _Kevin P. Thompson_, Dec 08 2021