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Numbers m for which sigma(m) - m = tau(m)^k for some integer k > 0.
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%I #30 Jul 31 2023 05:49:27

%S 4,26,56,90,122,568,2042,8186,32762,37432,68652,299576,2097146,

%T 8388602,19173944,33554426,67751984,78536544824,306296525088,

%U 15640174780344,39998905951528,120948840863188

%N Numbers m for which sigma(m) - m = tau(m)^k for some integer k > 0.

%C 39614081257132168796771975162 is also a term. - _Donovan Johnson_, Nov 28 2012

%C 19495118728903626376363904 = 2^7*152305615069559581065343 is a term. - _Martin Ehrenstein_, Jul 31 2023

%t f[n_] := FullSimplify[Log[DivisorSigma[1, n] - n]/Log[DivisorSigma[0, n]]]; Select[Range[2, 1000], IntegerQ[f[#]] && f[#] > 0 &] (* _T. D. Noe_, Nov 27 2012 *)

%Y Cf. A051281.

%K nonn,more

%O 1,1

%A _Zdenek Cervenka_, Nov 27 2012

%E a(16)-a(17) from _Donovan Johnson_, Nov 28 2012

%E a(18)-a(22) from _Martin Ehrenstein_, Jul 31 2023