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

2,3

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A051903, A129132, A359071 (numerators).

Sequence in context: A293221 A334512 A096625 * A263455 A283677 A355192

Adjacent sequences: A359069 A359070 A359071 * A359073 A359074 A359075

Keyword

nonn,frac

Author

Amiram Eldar, Dec 15 2022

Status

approved