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.
%I A046870 #19 Jun 15 2024 05:48:32
%S A046870 1,4,9,16,20,25,36,49,50,64,81,100,117,121,144,169,180,196,225,242,
%T A046870 256,289,324,325,361,400,441,450,468,484,500,529,576,578,605,625,650,
%U A046870 676,729,784,800,841,900,961,980,1024,1025,1058,1089,1156,1225,1280,1296
%N A046870 Numbers k such that sigma_1(k) divides sigma_4(k).
%C A046870 sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).
%C A046870 sigma_2(n) is the sum of the squares of the divisors of n (A001157).
%C A046870 sigma_4(n) is the sum of the 4th powers of the divisors of n (A001159).
%H A046870 Amiram Eldar, <a href="/A046870/b046870.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo P. Lava)
%e A046870 k = a(18) = 196 of which divisor power sums for k=0,1,2,3,4 are 9,399,51471, 8613489, 1574446419. sigma_1(k) = 399 and sigma_4(k) = 51471*30589=399*129*30589. Thus both sigma_2(k) and sigma_1(k) divide sigma_4(k).
%t A046870 Select[Range[1300], Divisible @@ DivisorSigma[{4, 1}, #] &] (* _Amiram Eldar_, Jun 15 2024 *)
%o A046870 (PARI) is(k) = {my(f = factor(k)); !(sigma(f, 4) % sigma(f)); } \\ _Amiram Eldar_, Jun 15 2024
%Y A046870 Cf. A000203, A001157, A001159.
%Y A046870 Has large overlap with A020487.
%K A046870 nonn
%O A046870 1,2
%A A046870 _Labos Elemer_