A116417 - OEIS

%I #22 Aug 20 2017 10:02:35

%S 1,1,2,2,3,3,6,6,4,4,4,4,12,12,12,12,5,5,10,10,15,15,30,30,20,20,20,

%T 20,60,60,60,60,6,6,3,3,2,2,1,1,12,12,12,12,4,4,4,4,30,30,15,15,10,10,

%U 5,5,60,60,60,60,20,20,20,20,7,7,14,14,21,21,42,42,28,28,28,28,84,84,84,84

%N If n = Sum_{m>=1} 2^(m-1) * b(n,m), where each b(n,m) is 0 or 1 and the sum is a finite sum, then a(n) = denominator of Sum_{m>=1} b(n,m)/m.

%H Peter Kagey, <a href="/A116417/b116417.txt">Table of n, a(n) for n = 0..10000</a>

%e 13 in binary is 1101. So a(13) is the denominator of 1/4 + 1/3 + 1 = 19/12, since the binary digits at positions (from right to left) 1, 3 and 4 are each 1 and the other digits are 0.

%t Table[Denominator@ Total@ MapIndexed[#1/ First@ #2 &, Reverse@ IntegerDigits[n, 2]], {n, 0, 79}] (* _Michael De Vlieger_, Aug 19 2017 *)

%o (PARI) a(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k));} \\ _Michel Marcus_, Apr 18 2016

%Y Cf. A007088, A116416, A271410.

%K easy,frac,nonn

%O 0,3

%A _Leroy Quet_, Feb 13 2006

%E More terms from _Joshua Zucker_, May 03 2006