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A210523 Record values of Dedekind psi function.

%I A210523 #22 Nov 26 2019 20:03:35
%S A210523 1,3,4,6,12,18,24,36,48,72,96,108,144,168,192,216,240,288,360,384,432,
%T A210523 576,648,672,720,864,1008,1152,1296,1344,1440,1728,1800,2016,2304,
%U A210523 2592,2880,3024,3456,4032,4320,4608,5184
%N A210523 Record values of Dedekind psi function.
%C A210523 Record values of A001615.
%H A210523 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 A210523 a(n) = A001615(A330006(n)). - _Amiram Eldar_, Nov 26 2019
%p A210523 N:= 100: # to get a(1) to a(N)
%p A210523 A001615 := proc(n) n*mul((1+1/i[1]), i=ifactors(n)[2]) end:
%p A210523 count:= 0:
%p A210523 val:= -infinity:
%p A210523 for i from 1 while count < N do
%p A210523   v:= A001615(i);
%p A210523   if v > val then
%p A210523      val:= v;
%p A210523        count:= count+1;
%p A210523        A[count]:=v;
%p A210523   fi
%p A210523 od:
%p A210523 seq(A[i],i=1..N); # _Robert Israel_, Nov 19 2014
%t A210523 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 A210523 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 A210523 Cf. A002183, A006093, A330006 (the corresponding positions of records).
%K A210523 nonn
%O A210523 1,2
%A A210523 _Enrique Pérez Herrero_, Jan 27 2013