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 A286972 #14 Jan 10 2025 12:14:57
%S A286972 2,3,4,5,7,9,11,12,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,42,43,
%T A286972 47,49,51,53,55,57,59,61,64,65,67,69,71,73,75,77,78,79,80,81,83,84,85,
%U A286972 87,89,91,93,95,97,100,101,103,105,107,108,109,110,111,113,114,115,119,121,123,127,129,131,132,133,135,137,139
%N A286972 Numbers k such that the average of the prime power divisors (not including 1) of k is an integer.
%C A286972 Numbers k such that A001222(k)|A023889(k).
%H A286972 Amiram Eldar, <a href="/A286972/b286972.txt">Table of n, a(n) for n = 1..10000</a>
%H A286972 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%e A286972 12 is in the sequence because 12 has 6 divisors {1, 2, 3, 4, 6, 12} among which 3 are prime powers {2, 3, 4} and (2 + 3 + 4)/3 = 3 is an integer.
%t A286972 fQ[n_] := IntegerQ@Mean@Select[Divisors@n, PrimePowerQ]; Select[Range@140, fQ]
%o A286972 (PARI) isok(m) = my(vd = select(isprimepower, divisors(m))); #vd && !(vecsum(vd) % #vd); \\ _Michel Marcus_, Apr 28 2020
%Y A286972 Cf. A001222, A003601, A023886, A023889, A078174, A246655, A285510.
%K A286972 nonn
%O A286972 1,1
%A A286972 _Ilya Gutkovskiy_, May 17 2017