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 A277793 #23 Feb 16 2025 08:33:37
%S A277793 1,49,169,361,961,1369,1849,3721,4489,5329,6241,8281,9409,10609,11881,
%T A277793 14641,16129,17689,19321,22801,24649,26569,32761,37249,39601,44521,
%U A277793 47089,49729,52441,58081,61009,67081,73441,76729,80089,87616,90601,94249,97969,109561,113569,121801,134689
%N A277793 Numbers k such that the arithmetic and geometric means of the divisors of k are both integers.
%C A277793 Intersection of A000290 and A003601.
%C A277793 Union of squares of A107924 and squares of A107925.
%C A277793 The squares of the primes == 1 (mod 6), squares of A002476, are a subsequence: 49, 169, 361,... - _R. J. Mathar_, May 19 2020
%H A277793 Amiram Eldar, <a href="/A277793/b277793.txt">Table of n, a(n) for n = 1..10000</a>
%H A277793 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Divisor.html">Divisor</a>
%H A277793 Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>
%H A277793 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%e A277793 a(2) = 49 because 49 has 3 divisors {1,7,49} therefore (1 + 7 + 49)/3 = 19 and (1*7*49)^(1/3) = 7 are both integers.
%t A277793 Select[Range[140000], Divisible[DivisorSigma[1, #1], DivisorSigma[0, #1]] && Mod[DivisorSigma[0, #1], 2] == 1 & ]
%t A277793 Select[Range[150000],AllTrue[{Mean[Divisors[#]],GeometricMean[ Divisors[ #]]}, IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 21 2018 *)
%Y A277793 Cf. A000290, A003601, A107924, A107925.
%K A277793 nonn,easy
%O A277793 1,2
%A A277793 _Ilya Gutkovskiy_, Oct 31 2016