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Record values of Dedekind psi function.
3

%I #22 Nov 26 2019 20:03:35

%S 1,3,4,6,12,18,24,36,48,72,96,108,144,168,192,216,240,288,360,384,432,

%T 576,648,672,720,864,1008,1152,1296,1344,1440,1728,1800,2016,2304,

%U 2592,2880,3024,3456,4032,4320,4608,5184

%N Record values of Dedekind psi function.

%C Record values of A001615.

%H Amiram Eldar, <a href="/A210523/b210523.txt">Table of n, a(n) for n = 1..808</a> (terms 1..373 from Enrique Pérez Herrero)

%F a(n) = A001615(A330006(n)). - _Amiram Eldar_, Nov 26 2019

%p N:= 100: # to get a(1) to a(N)

%p A001615 := proc(n) n*mul((1+1/i[1]), i=ifactors(n)[2]) end:

%p count:= 0:

%p val:= -infinity:

%p for i from 1 while count < N do

%p v:= A001615(i);

%p if v > val then

%p val:= v;

%p count:= count+1;

%p A[count]:=v;

%p fi

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Nov 19 2014

%t 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

%t 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 *)

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

%K nonn

%O 1,2

%A _Enrique Pérez Herrero_, Jan 27 2013