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Numbers k such that sigma(k) - phi(k) is a cube.
2

%I #11 Jun 29 2018 02:19:40

%S 1,30,44,87,169,247,515,630,707,910,1067,1255,1356,1691,2128,2188,

%T 2291,2438,2574,2627,2747,2867,3668,3689,4063,4295,5206,5359,5999,

%U 6331,6583,6835,7719,8286,8968,8991,9383

%N Numbers k such that sigma(k) - phi(k) is a cube.

%H Harry J. Smith, <a href="/A062385/b062385.txt">Table of n, a(n) for n = 1..1000</a>

%e sigma(30) - phi(30) = 72 - 8 = 64 = 4^3, so 30 is a term of the sequence.

%t Select[Range[10^4], IntegerQ[(DivisorSigma[1, # ] - EulerPhi[ # ])^(1/3)] &]

%o (PARI) select(k->ispower(sigma(k)-eulerphi(k), 3), [1..10000]) \\ _Harry J. Smith_, Aug 06 2009

%K nonn

%O 1,2

%A _Joseph L. Pe_, Feb 13 2002