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A092693
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Sum of iterated phi(n).
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7
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0, 1, 3, 3, 7, 3, 9, 7, 9, 7, 17, 7, 19, 9, 15, 15, 31, 9, 27, 15, 19, 17, 39, 15, 35, 19, 27, 19, 47, 15, 45, 31, 35, 31, 39, 19, 55, 27, 39, 31, 71, 19, 61, 35, 39, 39, 85, 31, 61, 35, 63, 39, 91, 27, 71, 39, 55, 47, 105, 31, 91, 45, 55, 63, 79, 35, 101, 63, 79, 39, 109, 39, 111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Iannucci, Moujie and Cohen examine perfect totient numbers: n such that a(n) = n.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Douglas E. Iannucci, Deng Moujie and Graeme L. Cohen, On Perfect Totient Numbers, J. Integer Sequences, 6 (2003), #03.4.5.
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FORMULA
| a(1) = 0, a(n) = phi(n) + a(phi(n))
a(n) = A053478(n) - n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 02 2004
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EXAMPLE
| a(100) = 71 because the iterations of phi (40, 16, 8, 4, 2, 1) sum to 71.
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MATHEMATICA
| nMax=100; a=Table[0, {nMax}]; Do[e=EulerPhi[n]; a[[n]]=e+a[[e]], {n, 2, nMax}]; a (* Noe *)
Table[Plus @@ FixedPointList[EulerPhi, n] - (n + 1), {n, 72}] (* Alonso Delarte (alonso.delarte(AT)gmail.com), Jan 29 2007 *)
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PROG
| (Haskell)
a092693 1 = 0
a092693 n = (+ 1) $ sum $ takeWhile (/= 1) $ iterate a000010 $ a000010 n
-- Reinhard Zumkeller, Oct 27 2011
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CROSSREFS
| Cf. A003434 (iterations of phi(n) needed to reach 1), A092694 (iterated phi product).
Cf. A082897 and A091847 (perfect totient numbers).
Sequence in context: A030316 A034257 A145501 * A134661 A135434 A204204
Adjacent sequences: A092690 A092691 A092692 * A092694 A092695 A092696
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Mar 04 2004
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