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 A374904 #8 Jul 23 2024 20:46:56
%S A374904 1,4,9,12,16,18,20,25,28,36,44,45,49,50,52,63,64,68,72,75,76,81,92,98,
%T A374904 99,100,108,116,117,121,124,144,147,148,153,164,169,171,172,175,180,
%U A374904 188,192,196,200,207,212,225,236,242,244,245,252,256,261,268,275,279
%N A374904 Numbers whose divisors have an integer mean number of divisors.
%C A374904 Numbers k such that A000005(k) | A007425(k).
%C A374904 Numbers k such that A374903(k) = 1.
%C A374904 If k is a term then all the numbers with the same prime signature as k are terms. The least terms of each prime signature are in A374905.
%C A374904 If {e_i} are the exponents in the prime factorization of k, then k is a term if and only if Product_{i} (e_i/2 + 1) is an integer.
%C A374904 1 is the only squarefree (A005117) term.
%C A374904 All the squares are terms.
%H A374904 Amiram Eldar, <a href="/A374904/b374904.txt">Table of n, a(n) for n = 1..10000</a>
%e A374904 4 is a term since it has 3 divisors, 1, 2 and 4, their numbers of divisors are 1, 2 and 3, and their mean is (1 + 2 + 3)/3 = 2 which is an integer.
%t A374904 f[p_, e_] := (e + 2)/2; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[300], q]
%o A374904 (PARI) is(n) = denominator(vecprod(apply(x -> x/2 +1, factor(n)[, 2]))) == 1;
%Y A374904 Cf. A000005, A005117, A007425, A374902, A374903.
%K A374904 nonn,easy
%O A374904 1,2
%A A374904 _Amiram Eldar_, Jul 23 2024