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 A165442 Start with m, repeatedly find sum of prime factors until we reach a fixed point, then compute sum of numbers in trajectory except for m and the fixed point. If the resulting sum equals m, adjoin m to the sequence. 0

%I #2 May 01 2013 21:12:46

%S 20,38,74

%N Start with m, repeatedly find sum of prime factors until we reach a fixed point, then compute sum of numbers in trajectory except for m and the fixed point. If the resulting sum equals m, adjoin m to the sequence.

%C No further terms below 10^13. Note that if the sum of the prime factors of a composite number equals itself, then it can only be 4.

%e Take 20 as example, the sum of its prime factors is 9, then we move on until we get a prime, 9=3x3, 3+3=6, and 6=2x3, 2+3=5, add all the results in the process, 9+6+5=20. 20=9+6+5, 38=21+10+7, 74=39+16+8+6+5.

%Y Cf. A001414, A029908.

%K nonn,more,bref

%O 1,1

%A K. T. Lee (7x3(AT)21cn.com), Sep 19 2009

%E Edited by _N. J. A. Sloane_, Sep 20 2009

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Last modified December 7 12:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)