cp's OEIS Frontend

A135772 Numbers having equal number of divisors and binary digits.

%I A135772 #15 Jul 30 2021 08:29:45
%S A135772 1,2,3,4,8,10,14,15,16,32,44,45,50,52,63,64,128,130,135,136,138,152,
%T A135772 154,165,170,174,182,184,186,189,190,195,222,230,231,232,238,246,248,
%U A135772 250,255,256,441,484,512,567,592,656,688,752,848,891,944,976
%N A135772 Numbers having equal number of divisors and binary digits.
%H A135772 G. C. Greubel, <a href="/A135772/b135772.txt">Table of n, a(n) for n = 1..1000</a>
%e A135772 a(1) = 1 since 1 has 1 divisor and 1 binary digit.
%e A135772 a(2), a(3) = 2, 3 since 2 = 10_2 and 3 = 11_2 have 2 divisors and 2 binary digits.
%e A135772 a(4) = 4 = 100_2 is the only number with 3 binary digits having 3 divisors.
%e A135772 8, 10, 14, 15 have 4 binary digits and 4 divisors.
%t A135772 Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 2] &] (* _G. C. Greubel_, Nov 08 2016 *)
%o A135772 (PARI) for(d=1,10,for(n=2^(d-1),2^d-1,d==numdiv(n)&print1(n", ")))
%o A135772 (Python)
%o A135772 from sympy import divisor_count
%o A135772 def ok(n): return divisor_count(n) == n.bit_length()
%o A135772 print(list(filter(ok, range(1, 977)))) # _Michael S. Branicky_, Jul 29 2021
%Y A135772 Cf. A000005, A070939.
%Y A135772 Cf. A135773, A135774, A135775, A135776, A135777, A135778, A135779, A095862.
%K A135772 base,nonn
%O A135772 1,2
%A A135772 _M. F. Hasler_, Nov 28 2007