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A108861 Numbers k that divide the sum of the digits of 2^k * k!. 2
1, 2, 3, 5, 6, 9, 27, 81, 126, 159, 205, 252, 254, 267, 285, 675, 1053, 1086, 1125, 1146, 2007, 5088, 5382, 5448, 14652, 23401, 23574, 24009, 41004, 66789, 67482, 111480, 866538, 1447875, 2413152, 2414019, 2417828, 2421360, 4045482, 6713982 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Next term after 5448 is greater than 10000.

a(34) > 10^6. - D. S. McNeil, Mar 03 2009

a(39) > 2.54 * 10^6, if it exists. - Kevin P. Thompson, Oct 20 2021

a(41) > 7*10^6, if it exists. - Kevin P. Thompson, Dec 08 2021

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

9 is a term because the sum of the digits of 2^9 * 9! = 185794560 is 45 which is divisible by 9.

MATHEMATICA

Do[If[Mod[Plus @@ IntegerDigits[2^n * n! ], n] == 0, Print[n]], {n, 1, 10000}]

PROG

(PARI) isok(k) = !(sumdigits(2^k * k!) % k); \\ Michel Marcus, Oct 20 2021

(Python)

from itertools import islice

def A108861(): # generator of terms

k, k2, kf = 1, 2, 1

while True:

c = sum(int(d) for d in str(k2*kf))

if not c % k: yield k

k += 1

k2 *= 2

kf *= k

A108861_list = list(islice(A108861(), 10)) # Chai Wah Wu, Oct 26 2021

CROSSREFS

Cf. A000165, A007953, A052582.

Sequence in context: A131761 A272776 A055690 * A294634 A051896 A061939

Adjacent sequences: A108858 A108859 A108860 * A108862 A108863 A108864

KEYWORD

nonn,base,hard,more

AUTHOR

Ryan Propper, Jul 11 2005

EXTENSIONS

a(25)-a(33) from D. S. McNeil, Mar 03 2009

a(34)-a(38) from Kevin P. Thompson, Oct 20 2021

a(39)-a(40) from Kevin P. Thompson, Dec 08 2021

STATUS

approved

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Last modified January 31 18:34 EST 2023. Contains 359980 sequences. (Running on oeis4.)