A370684 Numbers k such that there is no j with 2 <= j < k such that j*k divides binomial(k,j).

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.

Links

Table of n, a(n) for n=1..30.

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

Adjacent sequences: A370681 A370682 A370683 * A370685 A370686 A370687

Keyword

nonn,more

Author

Robert Israel, Feb 28 2024

Status

approved