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Search: id:A113808
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| A113808 |
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Positive integers n such that S(n) divides n, where S(n) is the sum of the iterates of the Euler phi-function of n, that is, S(n) = phi(n)+phi(phi(n))+....+ 1. |
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1
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| 1, 2, 3, 6, 9, 15, 18, 27, 30, 39, 54, 78, 81, 111, 162, 183, 222, 243, 255, 327, 363, 366, 471, 486, 510, 654, 726, 729, 942, 1458, 2187, 2199, 3063, 4359, 4374, 4375, 4398, 5571, 6126, 6561, 8718, 8750, 8751, 11142, 13122, 15723, 17502, 19683
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OFFSET
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1,2
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REFERENCES
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Igor E. Shparlinski, On the sum of iterations of the Euler function, Journal of Integer Sequences, Volume 9 (2006), Article 06.1.6.
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EXAMPLE
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18 is in the sequence because phi(18)+phi(phi(18))+phi(phi(phi(18))) = 6 + 2 + 1 = 9, which divides 18.
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CROSSREFS
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Cf. A082897.
Sequence in context: A115856 A032231 A114323 this_sequence A040040 A086642 A014214
Adjacent sequences: A113805 A113806 A113807 this_sequence A113809 A113810 A113811
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KEYWORD
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nonn
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AUTHOR
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Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Jan 22 2006
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