A330006 -id:A330006 - cp's OEIS frontend

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

Enrique Pérez Herrero, Jan 27 2013

nonn

Record values of A001615.

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

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

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

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 *)

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

A373320 Numbers k such that phi(k)/k^2 < phi(m)/m^2 for all m < k, where phi is the Euler totient function (A000010).

Original entry on oeis.org

1, 2, 3, 4, 6, 10, 12, 18, 24, 30, 42, 54, 60, 78, 84, 90, 114, 120, 150, 168, 180, 210, 270, 294, 300, 330, 390, 420, 510, 546, 570, 630, 750, 780, 840, 990, 1050, 1170, 1260, 1470, 1650, 1680, 1890, 2100, 2310, 2730, 3150, 3360, 3570, 3990, 4290, 4410, 4620

Offset: 1

Amiram Eldar, Jun 01 2024

nonn

First differs from A330006 at n = 52: a(52) = 4410 is not a term of A330006. The first term of A330006 that is not in this sequence is A330006(127) = 166530.
Numbers are less likely to be unitary divisors than any smaller number, i.e., numbers k such that the asymptotic density of numbers that are unitarily divided by k (A373318(k)/A373319(k)) is lower than the corresponding density of all m < k.
The numbers k such that phi(k)/k < phi(m)/m for all m < k are the primorial numbers (A002110).

Amiram Eldar, Table of n, a(n) for n = 1..670

Cf. A000010, A002110, A330006, A373318, A373319.

seq[kmax_] := Module[{rm = 2, r, s = {}}, Do[If[(r = EulerPhi[k]/k^2) < rm, rm = r; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[5000]

lista(kmax) = {my(rm = 2, r); for(k = 1, kmax, r = eulerphi(k)/k^2; if(r < rm, rm = r; print1(k, ", ")));}

cp's OEIS Frontend

A210523 Record values of Dedekind psi function.

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