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A354562
Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor.
6
6859, 11859210, 18253460, 38331320423, 41807225999, 49335445119, 50788425848, 67479324240, 203534609200, 245934780371, 250355343420, 581146348824, 779369813871, 1378677994836, 2152196307260, 2730426690524, 3616995855087, 5473549133744, 6213312123347, 6371699408179, 8817143116903
OFFSET
1,1
COMMENTS
Numbers k such that P(k)^3 | k and P(k+1)^3 | (k+1), where P(k) = A006530(k).
a(1)-a(5) and a(7) are from De Koninck (2009).
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.
EXAMPLE
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.
MATHEMATICA
q[n_] := FactorInteger[n][[-1, 2]] > 2; Select[Range[2*10^7], q[#] && q[# + 1] &]
PROG
(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
CROSSREFS
Subsequence of A070003, A354558 and A354561.
Intersection of A354563 and A354564.
Sequence in context: A066878 A176350 A114772 * A013811 A013892 A154086
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 30 2022
EXTENSIONS
a(6) and more terms from David A. Corneth, May 30 2022
STATUS
approved