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Numbers k such that k | sigma_6(k).
6

%I #33 Feb 25 2024 05:57:54

%S 1,10,26,60,65,130,150,228,260,442,650,780,876,988,1105,1140,1460,

%T 1690,1950,2210,2850,2964,3211,3796,4380,4420,4940,5070,5475,5548,

%U 6010,6422,8840,9633,10950,11050,11388,11972,12350,12818,13260,13756,14820,16644

%N Numbers k such that k | sigma_6(k).

%C sigma_6(k) is the sum of the 6th powers of the divisors of k (A013954).

%C Problem 11090 proves that this sequence is infinite. - _T. D. Noe_, Apr 18 2006

%H Amiram Eldar, <a href="/A055710/b055710.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..450 from Harvey P. Dale)

%H Florian Luca and John Ferdinands, <a href="http://www.jstor.org/stable/27641939">Problem 11090: Sometimes n divides sigma_k(n)</a>, Amer. Math. Monthly 113:4 (2006), pp. 372-373.

%t Do[If[Mod[DivisorSigma[6, n], n]==0, Print[n]], {n, 1, 25000}]

%t Select[Range[20000],Divisible[DivisorSigma[6,#],#]&] (* _Harvey P. Dale_, Jun 04 2015 *)

%o (PARI) is(n)=sigma(n,6)%n==0 \\ _Charles R Greathouse IV_, Feb 04 2013

%Y Cf. A013954.

%Y Cf. A055709, A055711, A055712, A055713.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Jun 09 2000