A354567 a(n) is the least number k such that P(k)^n | k and P(k+1)^n | (k+1), where P(k) = A006530(k) is the largest prime dividing k, or -1 if no such k exists.

1, 8, 6859, 11859210

Offset: 1

Author

Amiram Eldar, May 30 2022

Keywords

• nonn
• more
• bref

Comments

a(1) = 1 since P(1) = 1 by convention. Without this convention we would have a(1) = 2.

a(5) <= 437489361912143559513287483711091603378 (De Koninck, 2009).

Examples

			a(2) = 8 since 8 = 2^3, P(8) = 2 and 2^2|8, 9 = 3^2, P(9) = 3 and 3^2 | 9, and 8 is the least number with this property.
a(3) = 6859 since 6859 = 19^3, P(6859) = 19 and 19^3 | 6859, 6860 = 2^2 * 5 * 7^3, P(6860) = 7 and 7^3 | 6860, and 6859 is the least number with this property.
		

Links

• 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.

Crossrefs

Cf. A006530, A071178, A354558, A354562.