A271410 LCM of exponents in binary expansion of 2n.
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, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60, 60, 60, 60, 60, 60, 7, 7, 14, 14, 21, 21, 42
Offset: 0
Examples
a(2) = lcm(2) = 2 because 2*2 = 2^2; a(3) = lcm(1, 2) = 2 because 2*3 = 2^1 + 2^2; a(7) = lcm(1, 2, 3) = 6 because 2*7 = 2^3 + 2^2 + 2^1.
Links
- Peter Kagey, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
lcm[n_]:=Module[{idn2=IntegerDigits[n,2]},LCM@@Pick[Reverse[Range[ Length[ idn2]]], idn2,1]]; Join[{1},Array[lcm,100]] (* Harvey P. Dale, Jan 24 2019 *)
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PARI
a(n) = my(ve = select(x->x==1, Vecrev(binary(2*n)), 1)); lcm(vector(#ve, k, ve[k]-1)); \\ Michel Marcus, Apr 12 2016
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PARI
a(n)=lcm(Vec(select(x->x, Vecrev(binary(n)), 1))) \\ Charles R Greathouse IV, Apr 12 2016
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Python
from math import lcm def A271410(n): return lcm(*(i for i, b in enumerate(bin(n)[:1:-1],1) if b == '1')) # Chai Wah Wu, Dec 12 2022