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A330702
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Numbers k such that psi(k) = psi(k + 2) and phi(k) = phi(k + 2), where psi(k) is the Dedekind psi function (A001615) and phi(k) is the Euler totient function (A000010).
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1
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70, 308, 572, 2132, 4292, 6764, 12212, 32804, 72836, 79292, 169724, 198596, 207692, 289052, 362972, 392426, 545876, 547724, 611612, 651932, 678812, 687812, 809252, 842012, 868436, 930932, 1030772, 1032956, 1122932, 1336052, 1627772, 1705892, 1722932, 2173772
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OFFSET
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1,1
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COMMENTS
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Sandor asked whether this sequence is infinite.
Apparently the only common solution to psi(n) = psi(n+1) and phi(n) = phi(n+1) is 15.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..600
Jozsef Sandor, On the composition of some arithmetic functions, II, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, No. 3 (2005), Article 73.
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EXAMPLE
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70 is a term since psi(70) = psi (72) = 144 and phi(70) = phi(72) = 24.
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MATHEMATICA
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psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[10^5], psi[#] == psi[# + 2] && EulerPhi[#] == EulerPhi[#+2] &]
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CROSSREFS
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Intersection of A001494 and A330703.
Cf. A000010, A001615.
Sequence in context: A227879 A072596 A309310 * A335861 A174533 A174534
Adjacent sequences: A330699 A330700 A330701 * A330703 A330704 A330705
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, Dec 26 2019
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STATUS
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approved
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