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A135772
Numbers having equal number of divisors and binary digits.
12
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
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
KEYWORD
base,nonn
AUTHOR
M. F. Hasler, Nov 28 2007
STATUS
approved