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A179188
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Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010.
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14
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24, 34, 36, 39, 43, 44, 57, 72, 78, 82, 84, 93, 96, 108, 111, 146, 178, 201, 216, 222, 225, 226, 228, 306, 327, 364, 366, 381, 399, 417, 432, 438, 442, 466, 471, 482, 516, 527, 540, 543, 562, 576, 597, 610, 626, 633, 648, 706, 714, 732, 738, 802, 818, 866, 898, 912, 921, 924, 942, 948, 972, 1011
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OFFSET
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1,1
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COMMENTS
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There are 1385502728 terms under 10^12. - Jud McCranie, Feb 13 2012
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LINKS
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T. D. Noe and Jud McCranie, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
F. Firoozbakht, Puzzle 466. phi(n-1)=phi(n)=phi(n+1), in C. Rivera's Primepuzzles.
Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.
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FORMULA
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A000010(a(n)) = A000010(a(n)+6).
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MATHEMATICA
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Flatten[Position[Partition[EulerPhi[Range[1200]], 7, 1], _?(#[[1]] == #[[7]]&), {1}, Heads->False]] (* Harvey P. Dale, Jan 30 2016 *)
Select[Range[1000], EulerPhi[#] == EulerPhi[# + 6] &] (* Vincenzo Librandi, Sep 08 2016 *)
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PROG
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(PARI) {op=vector(N=6); for( n=1, 1e4, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}
(Magma) [n: n in [1..1000] | EulerPhi(n) eq EulerPhi(n+6)]; // Vincenzo Librandi, Sep 08 2016
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CROSSREFS
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Cf. A000010, A001274, A001494, A179186, A179187, A007015.
Sequence in context: A188671 A166648 A231468 * A102505 A112064 A090440
Adjacent sequences: A179185 A179186 A179187 * A179189 A179190 A179191
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, Jan 05 2011
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STATUS
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approved
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