A354563 Numbers k such that P(k)^2 | k and P(k+1)^3 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.

242, 2400, 6859, 10647, 47915, 57121, 344604, 499999, 830465, 1012499, 1431125, 2098853, 2825760, 2829123, 3930399, 5560691, 11859210, 12323584, 13137830, 18253460, 18279039, 21093749, 30664296, 32279841, 33999932, 37218852, 38640401, 38740085, 41485688, 45222737

Offset

1,1

Links

Daniel Suteu, Table of n, a(n) for n = 1..9503 (terms <= 10^15)

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 3^3 | 243.

Mathematica

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

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, 3)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 30 2022

Crossrefs

Subsequence of A070003 and A354558.

A354562 is a subsequence.

Cf. A006530, A071178, A354564.

Sequence in context: A234484 A160551 A258886 * A354565 A165935 A318529

Adjacent sequences: A354560 A354561 A354562 * A354564 A354565 A354566

Keyword

nonn

Author

Amiram Eldar, May 30 2022

Status

approved