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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.
3
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
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
EXTENSIONS
Edited by Dean Hickerson, Apr 09 2002
STATUS
approved