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

Author

M. F. Hasler, Nov 28 2007

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A070939.

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

Programs

Mathematica

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

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