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 A277553 #29 Jan 25 2025 03:15:30
%S A277553 1,20,49,169,361,500,605,961,980,1025,1369,1445,1700,1849,2645,3380,
%T A277553 3721,4205,4352,4489,4693,5329,6241,7220,8228,8281,8405,9409,9425,
%U A277553 10609,11045,11849,11881,12493,12500,14045,14580,14641,15125,16129,17405,17689,18785
%N A277553 Numbers k such that the sum of the divisors of k is divisible by the number of divisors of k, and the sum of the squares of the divisors of k is divisible by the sum of the divisors of k.
%C A277553 Numbers k such that A000005(k) divides A000203(k), and A000203(k) divides A001157(k).
%H A277553 Amiram Eldar, <a href="/A277553/b277553.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e A277553 1369 has 3 divisors which sum to 1407; 1407 is divisible by 3; the sum of the squares of the divisors of 1369 is 1875531 which is divisible by 1407; so 1369 is a term of the sequence.
%t A277553 Select[Range[50000],Divisible[DivisorSigma[1,#],DivisorSigma[0,#]] && Divisible[ DivisorSigma[2,#], DivisorSigma[1,#]]&]
%o A277553 (PARI) isok(k) = {my(f = factor(k), d = numdiv(f), s = sigma(f), s2 = sigma(f, 2)); !(s % d) && !(s2 % s);} \\ _Amiram Eldar_, Jan 25 2025
%Y A277553 Cf. A000005, A000203, A001157.
%Y A277553 Intersection of A003601 and A020487. See also A020486.
%K A277553 nonn
%O A277553 1,2
%A A277553 _Harvey P. Dale_, Oct 19 2016