A116417 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.
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, 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, 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
Offset: 0
Examples
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.
Links
- Peter Kagey, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
Table[Denominator@ Total@ MapIndexed[#1/ First@ #2 &, Reverse@ IntegerDigits[n, 2]], {n, 0, 79}] (* Michael De Vlieger, Aug 19 2017 *) -
PARI
a(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k));} \\ Michel Marcus, Apr 18 2016
Extensions
More terms from Joshua Zucker, May 03 2006