A303703 Positive numbers that are congruent mod k! to a divisor of k! for any k > 0.

1, 2, 3, 6, 8, 12, 24, 30, 60, 120, 144, 180, 240, 360, 720, 840, 1680, 2520, 5040, 5760, 6720, 10080, 20160, 40320, 45360, 60480, 90720, 120960, 181440, 362880, 403200, 453600, 725760, 907200, 1209600, 1814400, 3628800, 3991680

Offset: 1

Author

Rémy Sigrist, Apr 29 2018

Keywords

• nonn

Comments

This sequence is infinite as it contains all factorial numbers (A000142).

Examples

			8 == 1 mod 1! and 1 divides 1!, 8 == 2 mod 2! and 2 divides 2!, 8 == 2 mod 3! and 2 divides 3!, 8 divides k! for any k > 3, hence 8 appears in the sequence.
42 == 18 mod 4! and 18 is not a divisor of 4!, hence 42 does not appear in the sequence.
		

Links

• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142.

Programs

PARI

is(n) = my (f=1); for (k=1, oo, f*=k; if (f%n==0, return (1), (n%f) && (f%(n%f)), return (0)))