A183037 a(n) = A001511(n)*2^A001511(n) where A001511(n) equals the 2-adic valuation of 2n.

2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 384, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 896, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2

Offset: 1

Author

Paul D. Hanna, Dec 19 2010

Keywords

• nonn

Comments

2n/2^A001511(n) is odd for n >= 1, so that A001511(n) is logarithmic in nature.

Examples

			L.g.f.: A(x) = 2*x + 8*x^2/2 + 2*x^3/3 + 24*x^4/4 + 2*x^5/5 + 8*x^6/6 + 2*x^7/7 + 64*x^8/8 + 2*x^9/9 + 8*x^10/10 + ...
The g.f. of A183036 begins:
exp(A(x)) = 1 + 2*x + 6*x^2 + 10*x^3 + 24*x^4 + 38*x^5 + 74*x^6 + ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383

Crossrefs

Cf. A183036.

Programs

Mathematica

Array[# 2^# &[IntegerExponent[#, 2] + 1] &, 93] (* Michael De Vlieger, Nov 06 2018 *)

PARI

{a(n)=valuation(2*n,2)*2^valuation(2*n,2)}

Python

def A183037(n): return (m:=n&-n)*m.bit_length()<<1 # Chai Wah Wu, Jul 12 2022

Formula

Logarithmic derivative of A183036.