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A334083
Integers m such that all binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.
2
1, 2, 4, 16, 32, 64, 128, 256, 1024, 2048, 4096, 8192, 16384
OFFSET
1,2
COMMENTS
Integers m such that A334082(m) = 0.
All terms are powers of 2, but this is not a sufficient condition since A334082(8) = 1.
PROG
(PARI) isok(n) = sum(k=0, n, !is_A005153(binomial(n, k))) == 0;
(Python)
from itertools import count, islice
from math import comb
from sympy import factorint
def A334083_gen(): # generator of terms
for n in count(0):
m, flag = 1<<n, True
for k in range(1, m):
c = comb(m, k)
if c > 1:
l = (~c & c-1).bit_length()
if l>0:
P = (1<<l+1)-1
for p, e in factorint(c>>l).items():
if p > 1+P:
flag = False
break
P *= (p**(e+1)-1)//(p-1)
else:
flag = False
break
if flag:
yield m
A334083_list = list(islice(A334083_gen(), 10)) # Chai Wah Wu, Jul 05 2023
CROSSREFS
Cf. A005153 (practical numbers), A007318 (binomial coefficients).
Sequence in context: A036345 A032464 A171381 * A274497 A145119 A081411
KEYWORD
nonn,more
AUTHOR
Michel Marcus, Apr 14 2020
EXTENSIONS
a(9) from Jinyuan Wang, Apr 14 2020
a(10)-a(13) from Chai Wah Wu, Jul 05 2023
STATUS
approved