A291043 - OEIS

%I #32 Oct 15 2019 03:09:03

%S 4,8,14,15,32,44,45,62,63,75,135,188,195,567,608,663,704,825,956,957,

%T 1023,1034,1275,1334,1484,1634,1845,1935,2223,2534,2685,2751,2871,

%U 3195,3404,3843,3915,4994,7004,7315,7544,8024,8055,9207,10695,11205,11984,12032

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

%C The only solutions to psi(n) = psi(n+1) = psi(n+2) below 10^8 are 14, 44, 62, 956.

%C 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 Amiram Eldar, <a href="/A291043/b291043.txt">Table of n, a(n) for n = 1..5000</a>

%e 4 is in the sequence since psi(4) = psi(5) = 6.

%t psi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2 / d, {d, Divisors @ n}]];

%t Select[Range[12000], psi[#] == psi[# + 1] &]

%t 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 (PARI) a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);

%o isok(n) = a001615(n)==a001615(n+1) \\ _Altug Alkan_, Aug 17 2017, after _Charles R Greathouse IV_ at A001615

%Y Cf. A001274, A001615.

%K nonn

%O 1,1

%A _Amiram Eldar_, Aug 16 2017