A343889 Integer k of the pairs (k, m) ordered by m with 1 < k < m such that k has the same prime divisors as m, and, k+1 has the same prime divisors as m+1.

2, 6, 14, 30, 75, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534

Offset: 1

Author

Bernard Schott, May 03 2021

Keywords

• nonn
• hard
• more

Comments

First column of the array A343101.

Even integer 2^q - 2, q >= 2 is a term (A000918), and only 75 is known to be not of this form.

Examples

			The corresponding pair to a(4) = 30 is (30, 960) because 30 = 2 * 3 * 5 and 960 = 2^5 * 3 * 5 while 961 = 31^2.
The corresponding pair to a(5) = 75 is (75, 1215) because 75 = 3 * 5^2 and 1215 = 5 * 3^5, while 76 = 2^2 * 19 and 1216 = 2^6 * 19.
		

Links

• BxMO 2011, Third Benelux Mathematical Olympiad, Problème 1.
• Index to sequences related to Olympiads.

Crossrefs

Cf. A000918, A087914 (2nd column), A343101 (array).