A210523 Record values of Dedekind psi function.

1, 3, 4, 6, 12, 18, 24, 36, 48, 72, 96, 108, 144, 168, 192, 216, 240, 288, 360, 384, 432, 576, 648, 672, 720, 864, 1008, 1152, 1296, 1344, 1440, 1728, 1800, 2016, 2304, 2592, 2880, 3024, 3456, 4032, 4320, 4608, 5184

Offset: 1

Author

Enrique Pérez Herrero, Jan 27 2013

Keywords

• nonn

Comments

Record values of A001615.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..808 (terms 1..373 from Enrique Pérez Herrero)

Crossrefs

Cf. A002183, A006093, A330006 (the corresponding positions of records).

Programs

Maple

N:= 100: # to get a(1) to a(N)
A001615 := proc(n) n*mul((1+1/i[1]), i=ifactors(n)[2]) end:
count:= 0:
val:= -infinity:
for i from 1 while count < N do
  v:= A001615(i);
  if v > val then
     val:= v;
       count:= count+1;
       A[count]:=v;
  fi
od:
seq(A[i],i=1..N); # Robert Israel, Nov 19 2014

Mathematica

JordanTotient[n_,k_:1] := DivisorSum[n, #^k*MoebiusMu[n/#]&] /; (n>0) && IntegerQ[n]; DedekindPsi[n_] := JordanTotient[n,2]/EulerPhi[n]; a=1; lst={a}; Do[b=DedekindPsi[n]; If[b>a, a=b; AppendTo[lst,b]], {n,2000}]; lst
psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); seq = {}; pmax = 0; Do[pmax = psi[n]; If[p > pmax, pmax = p; AppendTo[seq, p]], {n, 1, 10^5}]; seq (* Amiram Eldar, Nov 26 2019 *)

Formula

a(n) = A001615(A330006(n)). - Amiram Eldar, Nov 26 2019