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Search: id:A053478
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| A053478 |
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Sum of iterates when A000010, Euler-Phi is iterated until fixed point 1. |
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+0
3
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| 1, 3, 6, 7, 12, 9, 16, 15, 18, 17, 28, 19, 32, 23, 30, 31, 48, 27, 46, 35, 40, 39, 62, 39, 60, 45, 54, 47, 76, 45, 76, 63, 68, 65, 74, 55, 92, 65, 78, 71, 112, 61, 104, 79, 84, 85, 132, 79, 110, 85, 114, 91, 144, 81, 126, 95, 112, 105, 164, 91, 152, 107, 118, 127, 144, 101
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n=2^w, the sum is 2^(w+1)-1.
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FORMULA
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Sum[Nest[Phi, n, j], {j, 1, x[n]}], where x[n] = number of steps to reach fixed value.
a(n) = n + a(phi(n)). a(n) = A092693(n) + n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 02 2004
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EXAMPLE
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If Phi is applied repeatedly to n = 91, the iterates {91,72,24,8,4,2,1} are obtained. Their sum is a(91)=91+72+24+8+4+2+1=202.
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MATHEMATICA
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f[n_] := Plus @@ Drop[ FixedPointList[ EulerPhi, n], -1]; Table[ f[n], {n, 66}] (from Robert G. Wilson v Dec 16 2004)
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CROSSREFS
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Cf. A000010, A010554, A049099, A049100, A049107, A049108.
Sequence in context: A047556 A015819 A084125 this_sequence A138037 A073934 A092150
Adjacent sequences: A053475 A053476 A053477 this_sequence A053479 A053480 A053481
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 14 2000
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