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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. 5

%I #11 Oct 26 2019 09:57:49

%S 6,9,16,78,126,161,253,497,715,949,981,1046,1054,1261,1331,1379,1405,

%T 1431,1509,1521,1611,1751,1863,1891,2171,2492,2681,2822,3095,3101,

%U 3249,3401,3592,3611,3653,3809,4186,4192,4385,4453,4501,4599,4907,5121,5146

%N 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.

%C A129316 is the first element of the pair.

%C A generalization of Ruth-Aaron pairs (A006145).

%H Amiram Eldar, <a href="/A129317/b129317.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A129316(n+1). - _Amiram Eldar_, Oct 26 2019

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

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

%K easy,nonn

%O 1,1

%A _Walter Kehowski_, Apr 09 2007

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