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.

20, 38, 74

Offset: 1

Author

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

Keywords

• nonn
• more
• bref

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A001414, A029908.

Extensions

Edited by N. J. A. Sloane, Sep 20 2009