A111936 Denominator of n-th term of the harmonic series after removal of all terms 1/m from Sum_{m=1..n} 1/m for which m contains a 9 in its decimal representation.
1, 2, 6, 12, 60, 20, 140, 280, 280, 3080, 9240, 120120, 120120, 40040, 80080, 1361360, 12252240, 2450448, 2450448, 2450448, 56360304, 56360304, 1409007600, 1409007600, 4227022800, 4227022800, 4227022800, 131037706800, 262075413600
Offset: 1
Examples
n=9: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/10 = 789/280, therefore a(9) = 280.
References
- G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 3, sect. 4, Problem 124.
Programs
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Magma
a:=[k:k in [1..100]| not 9 in Intseq(k)]; [Denominator( &+[1/a[m]: m in [1..n]]): n in [1..30] ]; // Marius A. Burtea, Dec 29 2019
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Mathematica
Denominator[Accumulate[DeleteCases[Table[1/n,{n,40}],?(MemberQ[ IntegerDigits[ Denominator[#]],9]&)]]] (* _Harvey P. Dale, Mar 05 2013 *)
Extensions
Definition edited by N. J. A. Sloane, Dec 30 2019
Comments