A267117 Numbers m such that in their prime factorization m = p_1^e_1 * ... * p_k^e_k, there is no digit-position in the base-2 representation of the exponents e_1 .. e_k such that in that position all those exponents would have 1-bit.

1, 12, 18, 20, 28, 44, 45, 48, 50, 52, 60, 63, 68, 75, 76, 80, 84, 90, 92, 98, 99, 112, 116, 117, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 162, 164, 171, 172, 175, 176, 180, 188, 192, 198, 204, 207, 208, 212, 220, 228, 234, 236, 240, 242, 244, 245, 252, 260, 261, 268, 272, 275, 276, 279, 284, 288, 292, 294, 300

Offset: 1

Author

Antti Karttunen, Feb 03 2016

Keywords

• nonn
• base

Comments

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 21, 261, 2824, 29144, 294233, 2951313, 29542282, 295514868, 2955441810, 29555347819, ... . Apparently, the asymptotic density of this sequence exists and equals 0.2955... . - Amiram Eldar, Sep 09 2022

Examples

			60 = 2^2 * 3^1 * 5^1 is included, as bitwise-anding together the binary representations of the exponents, "10", "01" and "01" results "00", zero.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Indices of zeros in A267115.

Cf. A054753 (subsequence), A191555 (subsequence after the initial 2).

Cf. also A267114, A268376.

Programs

Mathematica

{1}~Join~Select[Range@ 300, BitAnd @@ Map[Last, FactorInteger@ #] == 0 &] (* Michael De Vlieger, Feb 07 2016 *)

Extensions

Erroneous claim corrected by Antti Karttunen, Feb 07 2016