A354565 Numbers k such that P(k)^2 | k and P(k+1)^4 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.

242, 2400, 57121, 499999, 1012499, 2825760, 2829123, 11859210, 18279039, 21093749, 37218852, 38740085, 70799772, 96393374, 413428949, 642837222, 656356767, 675975026, 1065352364, 1333564323, 1418528255, 2654744949, 5547008142, 8576868299, 9515377949, 10022519999

Offset

1,1

Links

Daniel Suteu, Table of n, a(n) for n = 1..1908 (terms <= 10^17)

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

242 = 2 * 11^2 is a term since P(242) = 11 and 11^2 | 242, 243 = 3^5, P(243) = 3, and 3^4 | 243.

Mathematica

p[n_] := FactorInteger[n][[-1, 2]]; Select[Range[10^6], p[#] > 1 && p[# + 1] > 3 &]

Prog

(Python)
from sympy import factorint
def c(n, e): f = factorint(n); return f[max(f)] >= e
def ok(n): return n > 1 and c(n, 2) and c(n+1, 4)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 30 2022

Crossrefs

Subsequence of A070003, A354558 and A354563.

Cf. A006530, A071178, A354566.

Sequence in context: A160551 A258886 A354563 * A165935 A318529 A006601

Adjacent sequences: A354562 A354563 A354564 * A354566 A354567 A354568

Keyword

nonn

Author

Amiram Eldar, May 30 2022

Status

approved