A359072 - OEIS

%I #15 Feb 12 2023 16:31:28

%S 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,

%T 4,20,20,20,20,20,20,20,20,60,60,60,60,60,60,60,60,30,15,30,30,15,15,

%U 15,15,5,5,5,5,10,10,10,5,30,30,30,30,15,15,15,15,5,5

%N Denominators of the partial sums of the reciprocals of the maximal exponent in prime factorization of the positive integers (A051903).

%H Amiram Eldar, <a href="/A359072/b359072.txt">Table of n, a(n) for n = 2..10000</a>

%H Wolfgang Schwarz and Jürgen Spilker, <a href="https://doi.org/10.1515/9783110944648.221">A remark on some special arithmetical functions</a>, 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.

%H D. Suryanarayana and R. Chandra Rao, <a href="https://doi.org/10.1007/BF01223919">On the maximum and minimum exponents in factoring integers</a>, Archiv der Mathematik, Vol. 28, No. 1 (1977), pp. 261-269.

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = denominator(Sum_{k=2..n} 1/A051903(k)).

%t f[n_] := Max[FactorInteger[n][[;; , 2]]]; f[1] = 0; Denominator[Accumulate[Table[1/f[n], {n, 2, 100}]]]

%Y Cf. A051903, A129132, A359071 (numerators).

%K nonn,frac

%O 2,3

%A _Amiram Eldar_, Dec 15 2022