A359072 Denominators of the partial sums of the reciprocals of the maximal exponent in prime factorization of the positive integers (A051903).
1, 1, 2, 2, 2, 2, 6, 3, 3, 3, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4, 4, 4, 4, 4, 20, 20, 20, 20, 20, 20, 20, 20, 60, 60, 60, 60, 60, 60, 60, 60, 30, 15, 30, 30, 15, 15, 15, 15, 5, 5, 5, 5, 10, 10, 10, 5, 30, 30, 30, 30, 15, 15, 15, 15, 5, 5
Offset: 2
Links
- Amiram Eldar, Table of n, a(n) for n = 2..10000
- Wolfgang Schwarz and Jürgen Spilker, A remark on some special arithmetical functions, in: E. Laurincikas, E. Manstavicius and V. Stakenas (eds.), Analytic and Probabilistic Methods in Number Theory, Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996, New Trends in Probability and Statistics, Vol. 4, VSP BV & TEV Ltd. (1997), pp. 221-245.
- D. Suryanarayana and R. Chandra Rao, On the maximum and minimum exponents in factoring integers, Archiv der Mathematik, Vol. 28, No. 1 (1977), pp. 261-269.
- Index entries for sequences computed from exponents in factorization of n.
Programs
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Mathematica
f[n_] := Max[FactorInteger[n][[;; , 2]]]; f[1] = 0; Denominator[Accumulate[Table[1/f[n], {n, 2, 100}]]]
Formula
a(n) = denominator(Sum_{k=2..n} 1/A051903(k)).