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

1,1

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.

Cf. A006530, A071178.

Sequence in context: A066878 A176350 A114772 * A013811 A013892 A154086

Adjacent sequences: A354559 A354560 A354561 * A354563 A354564 A354565

Keyword

nonn

Author

Amiram Eldar, May 30 2022

Extensions

a(6) and more terms from David A. Corneth, May 30 2022

Status

approved