A129317 The second of the pair of consecutive integers k and k+1 such that sopfr(k) divides sopfr(k+1), where sopfr(k) is the sum of the prime factors of k, counting multiplicity.

6, 9, 16, 78, 126, 161, 253, 497, 715, 949, 981, 1046, 1054, 1261, 1331, 1379, 1405, 1431, 1509, 1521, 1611, 1751, 1863, 1891, 2171, 2492, 2681, 2822, 3095, 3101, 3249, 3401, 3592, 3611, 3653, 3809, 4186, 4192, 4385, 4453, 4501, 4599, 4907, 5121, 5146

Offset: 1

Author

Walter Kehowski, Apr 09 2007

Keywords

• easy
• nonn

Comments

A129316 is the first element of the pair.

A generalization of Ruth-Aaron pairs (A006145).

Examples

			a(6)=161 since sopfr(160)=sopfr(2^5*5)=10+5=15 and sopfr(161)=sopfr(7*23)=30.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A006145, A039752, A129316, A129318, A129319.

Formula

sopfr(k+1) mod sopfr(k) = 0.

a(n) = A129316(n+1). - Amiram Eldar, Oct 26 2019