A066419 Numbers k such that k! is not divisible by the sum of the decimal digits of k!.

432, 444, 453, 458, 474, 476, 485, 489, 498, 507, 509, 532, 539, 541, 548, 550, 552, 554, 555, 556, 560, 565, 567, 576, 593, 597, 603, 608, 609, 610, 611, 612, 613, 624, 630, 632, 634, 640, 645, 657, 663, 665, 683, 685, 686, 692, 698, 703, 706, 708, 714

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Matthew Conroy)

Dimitri Zucker, Factorial Fact Frenzy (!), Combo Class Youtube video (2022).

Example

The sum of the decimal digits of 5! is 1+2+0=3 and 3 divides 120, so 5 is not in the sequence.
The sum of the decimal digits of 432! is 3897 = (9)(433) and 3897 does not divide 432!, so 432 is in the sequence.

Mathematica

Select[Range[1000], !Divisible[Factorial[#], Total[IntegerDigits[Factorial[#]]]] &], (* Tanya Khovanova, Jun 13 2021 *)

Prog

(Python)
from math import factorial
def sd(n): return sum(map(int, str(n)))
def ok(f): return f%sd(f) != 0
print([n for n in range(1, 715) if ok(factorial(n))]) # Michael S. Branicky, Jun 13 2021
(PARI) isA066419(n) = (Mod(n!, sumdigits(n!)) != 0) \\ Jianing Song, Aug 26 2024

Crossrefs

Cf. A004152 (sum of digits of n!).

Sequence in context: A063463 A175026 A205192 * A245469 A069781 A337670

Adjacent sequences: A066416 A066417 A066418 * A066420 A066421 A066422

Keyword

base,easy,nonn

Author

Matthew Conroy, Dec 25 2001

Status

approved