A334084 - OEIS

A334084

Integers m such that only 2 binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.

1, 3, 5, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767

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OFFSET

1,2

COMMENTS

Integers m such that A334082(m) = m-1.

Integers of the form 2^k-1 (A000225) with k>0 are terms, but this condition is not necessary since 5 is a term.

LINKS

PROG

(PARI) isok(n) = sum(k=0, n, !is_A005153(binomial(n, k))) == n-1;

(Python)

from itertools import count, islice

from math import comb

from sympy import factorint

def A334084_gen(startvalue=1): # generator of terms >= startvalue

for n in count(max(startvalue, 1)):

for k in range(1, n):

c = comb(n, k)

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:

break

P *= (p**(e+1)-1)//(p-1)

else:

break

else:

yield n

A334084_list = list(islice(A334084_gen(), 10)) # Chai Wah Wu, Jul 05 2023

CROSSREFS

Cf. A005153 (practical numbers), A007318 (binomial coefficients).

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(11) from Jinyuan Wang, Apr 14 2020

a(12)-a(16) from Chai Wah Wu, Jul 05 2023

STATUS

approved