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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001274, A001615.

Sequence in context: A312242 A312243 A166054 * A312244 A182841 A312245

Adjacent sequences: A291040 A291041 A291042 * A291044 A291045 A291046

Keyword

nonn

Author

Amiram Eldar, Aug 16 2017

Status

approved