|
|
A303703
|
|
Positive numbers that are congruent mod k! to a divisor of k! for any k > 0.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence is infinite as it contains all factorial numbers (A000142).
|
|
LINKS
|
|
|
EXAMPLE
|
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.
|
|
PROG
|
(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)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|