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

4, 8, 14, 15, 32, 44, 45, 62, 63, 75, 135, 188, 195, 567, 608, 663, 704, 825, 956, 957, 1023, 1034, 1275, 1334, 1484, 1634, 1845, 1935, 2223, 2534, 2685, 2751, 2871, 3195, 3404, 3843, 3915, 4994, 7004, 7315, 7544, 8024, 8055, 9207, 10695, 11205, 11984, 12032

Offset: 1

Author

Amiram Eldar, Aug 16 2017

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001274, A001615.

Programs

Mathematica

psi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2 / d, {d, Divisors @ n}]];
Select[Range[12000], psi[#] == psi[# + 1] &]
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 *)

PARI

a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);
isok(n) = a001615(n)==a001615(n+1) \\ Altug Alkan, Aug 17 2017, after Charles R Greathouse IV at A001615