A069087 Numbers m such that (1/m)*Sum_{k=1..m} core(k) > phi(m) where core(n) = A007913(n) is the squarefree part of n: the smallest number such that n*a(n) is a square and phi(n) = A000010(n) is the Euler totient function.

2, 6, 12, 18, 24, 30, 36, 42, 48, 60, 66, 72, 78, 84, 90, 96, 102, 114, 120, 126, 132, 138, 144, 150, 156, 168, 174, 180, 186, 198, 204, 210, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 294, 300, 306, 312, 318, 330, 336, 342, 348, 360, 372, 378, 390

Offset: 1

Author

Benoit Cloitre, Apr 05 2002

Keywords

• nonn

Comments

Equivalently, numbers m such that A069891(m) > m*phi(m).

The listed terms are all even, but there are some odd terms, including m = 111546435 = 3*5*7*11*13*17*19*23, for which A069891(m) = 4093453424286382 and m*phi(m) = 4070927302041600.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Programs

Mathematica

f[p_, e_] := If[OddQ[e], p, 1]; sqf[n_] := Times @@ (f @@@ FactorInteger[n]); seq = {}; s = 0; Do[s += sqf[n]; If[s > n*EulerPhi[n], AppendTo[seq, n]], {n, 1, 400}]; seq (* Amiram Eldar, Apr 02 2020 *)

PARI

is(n)=sum(k=1,n,core(k)) > n*eulerphi(n) \\ Charles R Greathouse IV, Feb 21 2013

Extensions

Edited by Dean Hickerson, Apr 09 2002