A354559 - OEIS

%I #19 Jun 05 2022 08:28:48

%S 1,2,5,13,28,79,204,549,1509,4231,12072,36426,112589

%N The number of terms of A354558 that are <= 10^n.

%C The data is from De Koninck et al. (2013).

%H Jean-Marie De Koninck, Nicolas Doyon, and Florian Luca, <a href="https://www.jeanmariedekoninck.mat.ulaval.ca/fileadmin/jmdk/Documents/Publications/2013_consecutive_integers_divisible_by_the_square_of_their_largest_prime_factors.pdf">Consecutive integers divisible by the square of their largest prime factors</a>, Journal of Combinatorics and Number Theory, Vol. 5, No. 2 (2013), pp. 81-93; <a href="https://www.researchgate.net/publication/268171058_Consecutive_integers_divisible_by_the_square_of_their_largest_prime_factors">Researchgate link</a>.

%H Jean-Marie De Koninck and Matthieu Moineau, <a href="http://emis.muni.cz/journals/JIS/VOL21/DeKoninck/dek22.html">Consecutive Integers Divisible by a Power of their Largest Prime Factor</a>, J. Integer Seq., Vol. 21 (2018), Article 18.9.3.

%H Régis de la Bretèche and Sary Drappeau, <a href="https://doi.org/10.4171/jems/951">Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables</a>, Journal of the European Mathematical Society, Vol. 22, No. 5 (2020), pp. 1577-1624; <a href="https://arxiv.org/abs/1703.03197">arXiv preprint</a>, arXiv:1703.03197 [math.NT], 2017-2019.

%e There is one term <= 10 in A354558, 8, therefore a(1) = 1.

%e There are 2 terms <= 10^2 in A354558, 8 and 49, therefore a(2) = 2.

%t 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])

%Y Cf. A354558.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, May 30 2022

%E a(12) from _Daniel Suteu_, Jun 03 2022

%E a(13) from _Daniel Suteu_, Jun 05 2022