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A370684
Numbers k such that there is no j with 2 <= j < k such that j*k divides binomial(k,j).
0
1, 2, 3, 4, 6, 7, 8, 12, 14, 15, 16, 18, 22, 23, 24, 30, 36, 40, 42, 44, 48, 63, 70, 72, 80, 90, 95, 96, 120, 240
OFFSET
1,2
COMMENTS
Numbers k such that A051574(k) = 1.
The only term == 1 (mod 4) is 1.
No more terms <= 10^7.
EXAMPLE
a(5) = 6 is a term because 2 * 6 does not divide binomial(6,2) = 15, 3 * 6 does not divide binomial(6,3) = 20, 4 * 6 does not divide binomial(6,4) = 15, and 5 * 6 does not divide binomial(6,5) = 6.
MAPLE
filter:= proc(n)
andmap(t -> binomial(n, t) mod (t*n) <> 0, [$2..n-1])
end proc:
select(filter, [$1..1000]);
PROG
(Python)
from itertools import count, islice
from math import comb
def A370684_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda k:all(comb(k, j)%(j*k) for j in range(2, k)), count(max(startvalue, 1)))
A370684_list = list(islice(A370684_gen(), 20)) # Chai Wah Wu, Feb 29 2024
CROSSREFS
Cf. A051574.
Sequence in context: A191282 A191281 A032900 * A268415 A352084 A277779
KEYWORD
nonn,more
AUTHOR
Robert Israel, Feb 28 2024
STATUS
approved