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

Author

Matthew Conroy, Dec 25 2001

Keywords

• base
• easy
• nonn

Examples

			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.
		

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).

Crossrefs

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

Programs

Mathematica

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

PARI

isA066419(n) = (Mod(n!, sumdigits(n!)) != 0) \\ Jianing Song, Aug 26 2024

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