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

1,1

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

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 *)

Prog

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

Crossrefs

Sequence in context: A066080 A319270 A071707 * A367504 A304450 A085345

Adjacent sequences: A069084 A069085 A069086 * A069088 A069089 A069090

Keyword

nonn

Author

Benoit Cloitre, Apr 05 2002

Extensions

Edited by Dean Hickerson, Apr 09 2002

Status

approved