cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A055712 Numbers k such that k | sigma_8(k).

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%I A055712 #28 Feb 25 2024 05:58:02
%S A055712 1,84,156,204,364,476,514,1092,1428,2316,2652,2892,6069,6188,6748,
%T A055712 12138,12532,16212,16388,18564,20244,24276,30108,37596,39372,49164,
%U A055712 63291,78897,87724,99202,114716,126582,147679,157794,167331
%N A055712 Numbers k such that k | sigma_8(k).
%C A055712 sigma_8(k) is the sum of the 8th powers of the divisors of k (A013956).
%C A055712 Problem 11090 proves that this sequence is infinite. - _T. D. Noe_, Apr 18 2006
%H A055712 Amiram Eldar, <a href="/A055712/b055712.txt">Table of n, a(n) for n = 1..1000</a>
%H A055712 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 A055712 Do[If[Mod[DivisorSigma[8, n], n]==0, Print[n]], {n, 1, 10000}]
%t A055712 Select[Range[170000],Divisible[DivisorSigma[8,#],#]&] (* _Harvey P. Dale_, Sep 15 2019 *)
%o A055712 (PARI) is(n)=sigma(n,8)%n==0 \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A055712 Cf. A013956.
%Y A055712 Cf. A055709, A055710, A055711, A055713.
%K A055712 nonn
%O A055712 1,2
%A A055712 _Robert G. Wilson v_, Jun 09 2000