A135772 Numbers having equal number of divisors and binary digits.

1, 2, 3, 4, 8, 10, 14, 15, 16, 32, 44, 45, 50, 52, 63, 64, 128, 130, 135, 136, 138, 152, 154, 165, 170, 174, 182, 184, 186, 189, 190, 195, 222, 230, 231, 232, 238, 246, 248, 250, 255, 256, 441, 484, 512, 567, 592, 656, 688, 752, 848, 891, 944, 976

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

a(1) = 1 since 1 has 1 divisor and 1 binary digit.
a(2), a(3) = 2, 3 since 2 = 10_2 and 3 = 11_2 have 2 divisors and 2 binary digits.
a(4) = 4 = 100_2 is the only number with 3 binary digits having 3 divisors.
8, 10, 14, 15 have 4 binary digits and 4 divisors.

Mathematica

Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 2] &] (* G. C. Greubel, Nov 08 2016 *)

Prog

(PARI) for(d=1, 10, for(n=2^(d-1), 2^d-1, d==numdiv(n)&print1(n", ")))
(Python)
from sympy import divisor_count
def ok(n): return divisor_count(n) == n.bit_length()
print(list(filter(ok, range(1, 977)))) # Michael S. Branicky, Jul 29 2021

Crossrefs

Cf. A000005, A070939.

Cf. A135773, A135774, A135775, A135776, A135777, A135778, A135779, A095862.

Sequence in context: A180941 A190896 A365018 * A209064 A222264 A051783

Adjacent sequences: A135769 A135770 A135771 * A135773 A135774 A135775

Keyword

base,nonn

Author

M. F. Hasler, Nov 28 2007

Status

approved