A354562 Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor.
6859, 11859210, 18253460, 38331320423, 41807225999, 49335445119, 50788425848, 67479324240, 203534609200, 245934780371, 250355343420, 581146348824, 779369813871, 1378677994836, 2152196307260, 2730426690524, 3616995855087, 5473549133744, 6213312123347, 6371699408179, 8817143116903
Offset: 1
Keywords
Examples
6859 = 19^3 is a term since P(6859) = 19 and 19^3 | 6859, 6860 = 2^2 * 5 * 7^3, P(6860) = 7 and 7^3 | 6860.
Links
- David A. Corneth, Table of n, a(n) for n = 1..81 (terms <= 10^15)
- Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 173, entry 6859.
- 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.
Crossrefs
Programs
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Mathematica
q[n_] := FactorInteger[n][[-1, 2]] > 2; Select[Range[2*10^7], q[#] && q[# + 1] &]
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Python
from sympy import factorint def c(n): f = factorint(n); return f[max(f)] >= 3 def ok(n): return n > 1 and c(n) and c(n+1) print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, May 30 2022
Extensions
a(6) and more terms from David A. Corneth, May 30 2022
Comments