A219668 Numbers m for which sigma(m) - m = tau(m)^k for some integer k > 0.

4, 26, 56, 90, 122, 568, 2042, 8186, 32762, 37432, 68652, 299576, 2097146, 8388602, 19173944, 33554426, 67751984, 78536544824, 306296525088, 15640174780344, 39998905951528, 120948840863188

Offset: 1

Author

Zdenek Cervenka, Nov 27 2012

Keywords

• nonn
• more

Comments

39614081257132168796771975162 is also a term. - Donovan Johnson, Nov 28 2012

19495118728903626376363904 = 2^7*152305615069559581065343 is a term. - Martin Ehrenstein, Jul 31 2023

Crossrefs

Cf. A051281.

Programs

Mathematica

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 *)

Extensions

a(16)-a(17) from Donovan Johnson, Nov 28 2012

a(18)-a(22) from Martin Ehrenstein, Jul 31 2023