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.

A046763 Numbers that divide the sum of cubes of their divisors.

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%I A046763 #39 Feb 17 2024 10:32:30
%S A046763 1,6,42,120,168,270,280,312,496,672,728,840,1080,1560,1782,1806,1890,
%T A046763 2044,2184,2520,3472,3640,3913,4256,5880,6048,6552,6615,7224,7560,
%U A046763 7826,8128,9120,9424,9933,10804,10920,11400,12040,12768,13230,13626,14040
%N A046763 Numbers that divide the sum of cubes of their divisors.
%C A046763 Compare with multiply perfect numbers, A007691. Here Sum(divisors) is replaced by Sum(cube of divisors).
%C A046763 Problem 11090 proves that this sequence is infinite. - _T. D. Noe_, Apr 18 2006
%C A046763 Tomohiro Yamada found that the odd number 209195 is a term. (See the Editorial Comment after the solution to Problem 11090.) - _Jonathan Sondow_, Nov 23 2012
%H A046763 Amiram Eldar, <a href="/A046763/b046763.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A046763 Florian Luca and John Ferdinands, <a href="https://www.jstor.org/stable/27641939">Problem 11090: Sometimes n divides sigma_k(n)</a>, Amer. Math. Monthly 113:4 (2006), pp. 372-373.
%e A046763 For k = 168 = a(5), Sum(d^3) = 5634720 = 33540*168 = 33540*k;
%t A046763 Select[Range[10^4], Divisible[DivisorSigma[3, #], #] &] (* _Amiram Eldar_, Sep 10 2019 *)
%o A046763 (PARI) is(n)=sigma(n,3)%n==0 \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A046763 Cf. A001158, A007691.
%K A046763 nonn
%O A046763 1,2
%A A046763 _Labos Elemer_