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

1,1

Comments

A129316 is the first element of the pair.

A generalization of Ruth-Aaron pairs (A006145).

Links

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

Formula

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

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

Example

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

Mathematica

Rest[Flatten[Position[Partition[Table[Total[Times@@@FactorInteger[n]], {n, 6000}], 2, 1], _?(Mod[#[[2]], #[[1]]]==0&), 1, Heads->False]]]+1 (* Harvey P. Dale, May 19 2026 *)

Crossrefs

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

Sequence in context: A290791 A132107 A007262 * A316067 A316068 A327796

Adjacent sequences: A129314 A129315 A129316 * A129318 A129319 A129320

Keyword

easy,nonn

Author

Walter Kehowski, Apr 09 2007

Status

approved