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A291043 Numbers n such that psi(n) = psi(n+1), where psi(n) is Dedekind psi function (A001615).

%I A291043 #32 Oct 15 2019 03:09:03
%S A291043 4,8,14,15,32,44,45,62,63,75,135,188,195,567,608,663,704,825,956,957,
%T A291043 1023,1034,1275,1334,1484,1634,1845,1935,2223,2534,2685,2751,2871,
%U A291043 3195,3404,3843,3915,4994,7004,7315,7544,8024,8055,9207,10695,11205,11984,12032
%N A291043 Numbers n such that psi(n) = psi(n+1), where psi(n) is Dedekind psi function (A001615).
%C A291043 The only solutions to psi(n) = psi(n+1) = psi(n+2) below 10^8 are 14, 44, 62, 956.
%C A291043 In this sequence, smallest terms k such that k and k + 1 are both product of m + 1 distinct primes are 14, 1334, 84134, 3571905, 424152105 for 1 <= m <= 5. - _Altug Alkan_, Aug 17 2017
%H A291043 Amiram Eldar, <a href="/A291043/b291043.txt">Table of n, a(n) for n = 1..5000</a>
%e A291043 4 is in the sequence since psi(4) = psi(5) = 6.
%t A291043 psi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2 / d, {d, Divisors @ n}]];
%t A291043 Select[Range[12000], psi[#] == psi[# + 1] &]
%t A291043 SequencePosition[Table[If[n<1,0,n Sum[MoebiusMu[d]^2/d,{d,Divisors[n]}]],{n,13000}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 22 2018 *)
%o A291043 (PARI) a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);
%o A291043 isok(n) = a001615(n)==a001615(n+1) \\ _Altug Alkan_, Aug 17 2017, after _Charles R Greathouse IV_ at A001615
%Y A291043 Cf. A001274, A001615.
%K A291043 nonn
%O A291043 1,1
%A A291043 _Amiram Eldar_, Aug 16 2017