A271984 Numbers n such that the denominator of the sum of the reciprocals of the exponents in the binary expansion of 2n is not equal to their LCM. That is, A271410(n) != A116417(n).

34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 98, 99, 100, 101, 102, 103, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 124, 125, 126, 127, 164, 165, 166, 167, 172, 173, 174, 175, 180, 181, 182, 183, 188, 189, 190, 191

Offset: 1

Author

Peter Kagey, Apr 17 2016

Keywords

• nonn
• base
• easy

Comments

a(2*n) = 1 + a(2*n-1) for all n > 0.

Examples

			a(1) = 34 because 34*2 = 68 is the first number such that the LCM of the exponents in its binary expansion (2 and 6) is unequal to the denominator of the sum of reciprocals: lcm(2, 6) = 6 != denominator(1/2 + 1/6) = 3.
Equivalently, A271410(34) = 6 != A116417(34) = 3.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A116417, A271410.

Programs

Mathematica

Select[Range@ 1000, (LCM @@ # != Denominator[ Total[1/#]]) &@ Flatten@ Position[ Reverse@ IntegerDigits[#, 2], 1] &] (* Giovanni Resta, Apr 18 2016 *)