A354560 Numbers k such that k, k+1 and k+2 are all divisible by the square of their largest prime factor.

1294298, 9841094, 158385500, 1947793550, 5833093013, 11587121710, 20944167840, 22979821310, 24604784814, 267631935500, 290672026412, 956544588350, 987988937343, 2399283556900, 2816075601855, 4174608151758, 4322550249043, 6789218799999, 10617595679778, 16036630184409

Offset: 1

Author

Amiram Eldar, May 30 2022

Keywords

• nonn

Comments

Numbers k such that P(k)^2 | k, P(k+1)^2 | (k+1), and P(k+2)^2 | (k+2), where P(k) = A006530(k).

The data is from De Koninck and Moineau (2018).

Examples

			1294298 = 2 * 61 * 103^2 is a term since P(1294298) = 103 and 103^2 | 1294298, 1294299 = 3^4 * 19 * 29^2, P(1294299) = 29 and 29^2 | 1294299, 1294300 = 2^2 * 5^2 * 7 * 43^2, P(1294300) = 43 and 43^2 | 1294300.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..60
• Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 277, entry 1294298.
• 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; Known members of E_{3,2} with at most 21 digits, addendum, 2025.

Crossrefs

Subsequence of A070003 and A354558.

Cf. A006530, A071178.