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

1,1

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).

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.

Example

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.

Crossrefs

Subsequence of A070003 and A354558.

Cf. A006530, A071178.

Sequence in context: A206749 A244563 A163681 * A185776 A345083 A345084

Adjacent sequences: A354557 A354558 A354559 * A354561 A354562 A354563

Keyword

nonn

Author

Amiram Eldar, May 30 2022

Status

approved