%I #22 Jul 06 2023 01:52:38
%S 1,2,4,16,32,64,128,256,1024,2048,4096,8192,16384
%N Integers m such that all binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.
%C Integers m such that A334082(m) = 0.
%C All terms are powers of 2, but this is not a sufficient condition since A334082(8) = 1.
%o (PARI) isok(n) = sum(k=0, n, !is_A005153(binomial(n,k))) == 0;
%o (Python)
%o from itertools import count, islice
%o from math import comb
%o from sympy import factorint
%o def A334083_gen(): # generator of terms
%o for n in count(0):
%o m, flag = 1<<n, True
%o for k in range(1,m):
%o c = comb(m,k)
%o if c > 1:
%o l = (~c & c-1).bit_length()
%o if l>0:
%o P = (1<<l+1)-1
%o for p, e in factorint(c>>l).items():
%o if p > 1+P:
%o flag = False
%o break
%o P *= (p**(e+1)-1)//(p-1)
%o else:
%o flag = False
%o break
%o if flag:
%o yield m
%o A334083_list = list(islice(A334083_gen(),10)) # _Chai Wah Wu_, Jul 05 2023
%Y Cf. A005153 (practical numbers), A007318 (binomial coefficients).
%Y Cf. A334082, A334084.
%K nonn,more
%O 1,2
%A _Michel Marcus_, Apr 14 2020
%E a(9) from _Jinyuan Wang_, Apr 14 2020
%E a(10)-a(13) from _Chai Wah Wu_, Jul 05 2023