A330702 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).
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
Offset: 1
Keywords
Examples
70 is a term since psi(70) = psi (72) = 144 and phi(70) = phi(72) = 24.
Links
- 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.
Programs
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Mathematica
psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[10^5], psi[#] == psi[# + 2] && EulerPhi[#] == EulerPhi[#+2] &]
Comments