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%I #31 Feb 21 2024 01:44:47
%S 1,6,22,28,66,120,198,264,308,366,440,604,672,924,984,1320,1464,1694,
%T 1717,2013,2296,2464,2574,2970,3434,3608,3960,4026,4228,4598,4920,
%U 5082,5151,5348,6200,6600,6644,6776,6868,6888,7320,7392,8052,8128,9504
%N Numbers k such that k | sigma_5(k).
%C sigma_5(k) is the sum of the 5th powers of the divisors of k (A001160).
%C Problem 11090 proves that this sequence is infinite. - _T. D. Noe_, Apr 18 2006
%H Charles R Greathouse IV, <a href="/A055709/b055709.txt">Table of n, a(n) for n = 1..7000</a>
%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[5, n], n]==0, Print[n]], {n, 1, 15000}]
%t Select[Range[10000],Divisible[DivisorSigma[5,#],#]&] (* _Harvey P. Dale_, Aug 09 2013 *)
%o (PARI) is(n)=sigma(n,5)%n==0 \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A001160.
%Y Cf. A055710, A055711, A055712, A055713.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jun 09 2000
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