A354559 The number of terms of A354558 that are <= 10^n.
1, 2, 5, 13, 28, 79, 204, 549, 1509, 4231, 12072, 36426, 112589
Offset: 1
Examples
There is one term <= 10 in A354558, 8, therefore a(1) = 1. There are 2 terms <= 10^2 in A354558, 8 and 49, therefore a(2) = 2.
Links
- Jean-Marie De Koninck, Nicolas Doyon, and Florian Luca, Consecutive integers divisible by the square of their largest prime factors, Journal of Combinatorics and Number Theory, Vol. 5, No. 2 (2013), pp. 81-93; Researchgate link.
- Jean-Marie De Koninck and Matthieu Moineau, Consecutive Integers Divisible by a Power of their Largest Prime Factor, J. Integer Seq., Vol. 21 (2018), Article 18.9.3.
- Régis de la Bretèche and Sary Drappeau, Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables, Journal of the European Mathematical Society, Vol. 22, No. 5 (2020), pp. 1577-1624; arXiv preprint, arXiv:1703.03197 [math.NT], 2017-2019.
Crossrefs
Cf. A354558.
Programs
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Mathematica
q[n_] := FactorInteger[n][[-1, 2]] > 1; c[s_, n_] := Count[s, _?(# <= n &)]; m = 6; c[Select[Range[10^m], q[#] && q[# + 1] &], #] & /@ (10^Range[m])
Extensions
a(12) from Daniel Suteu, Jun 03 2022
a(13) from Daniel Suteu, Jun 05 2022
Comments