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%I #40 Feb 29 2024 14:40:04
%S 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,
%T 90,95,96,120,240
%N Numbers k such that there is no j with 2 <= j < k such that j*k divides binomial(k,j).
%C Numbers k such that A051574(k) = 1.
%C The only term == 1 (mod 4) is 1.
%C No more terms <= 10^7.
%e 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.
%p filter:= proc(n)
%p andmap(t -> binomial(n,t) mod (t*n) <> 0, [$2..n-1])
%p end proc:
%p select(filter, [$1..1000]);
%o (Python)
%o from itertools import count, islice
%o from math import comb
%o def A370684_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda k:all(comb(k,j)%(j*k) for j in range(2,k)),count(max(startvalue,1)))
%o A370684_list = list(islice(A370684_gen(),20)) # _Chai Wah Wu_, Feb 29 2024
%Y Cf. A051574.
%K nonn,more
%O 1,2
%A _Robert Israel_, Feb 28 2024
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