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Search: id:A069823
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| A069823 |
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Nonprime n such there is no x<n such that phi(x)=phi(n). |
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+0
1
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| 1, 15, 25, 35, 51, 65, 69, 81, 85, 87, 121, 123, 129, 141, 143, 159, 161, 177, 185, 187, 203, 213, 235, 247, 249, 253, 255, 265, 267, 275, 289, 299, 301, 309, 321, 323, 339, 341, 343, 361, 393, 403, 415, 425, 447, 485, 489, 501, 519, 527, 529, 535, 537, 551
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If p is prime there is no x<p such that phi(x)=phi(p)=p-1 since phi(x)<p-1
Nonprime numbers n such that A081373[n]=1; i.e. number of numbers not exceeding n and with identical value of their phi than that of n, equals one. - Labos E. (labos(AT)ana.sote.hu), Mar 24 2003
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EXAMPLE
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n=25, a nonprime; phi values for k<=25 are {1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8,12,10,22,8,20}; no phi[k] except phi[25] equals 20, A081373[25]=1; if n was prime then A081373[n]=1 holds.
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MATHEMATICA
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f[x_] := EulerPhi[x] fc[x_] := Count[Table[f[j]-f[x], {j, 1, x}], 0] t1=Flatten[Position[Table[fc[w], {w, 1, 1000}], 1]] t2=Flatten[Position[PrimeQ[t1], False]] Part[t1, t2]
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PROGRAM
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(PARI) for(s=2, 600, if((1-isprime(s))*abs(prod(i=1, s-1, eulerphi(i)-eulerphi(s)))>0, print1(s, ", ")))
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CROSSREFS
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Cf. A081373, A067004, A000010.
Sequence in context: A102802 A050692 A050693 this_sequence A133321 A118960 A031888
Adjacent sequences: A069820 A069821 A069822 this_sequence A069824 A069825 A069826
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 28 2002
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