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%I #9 Aug 05 2019 06:37:23
%S 1,9,36,180,225,441,450,468,625,1089,1476,1521,1620,1800,2025,2178,
%T 2340,2601,3249,3600,4050,4500,4761,5202,5625,6561,7569,8100,8649,
%U 8712,9522,10000,12321,13572,15129,15138,16200,16641,19881,20808,22500,23400,25281,26244,28224,28800
%N Numbers n such that the sum of the divisors of n divides sum of squares of divisors of n and number of divisors of n divides n.
%C Intersection of A020487 and A033950.
%C Numbers n such that A000203(n)|A001157(n) and A000005(n)|n.
%H Amiram Eldar, <a href="/A280353/b280353.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%e 9 is in the sequence because 9 has 3 divisors {1,3,9}, 9/3 = 3 and (1^2 + 3^2 + 9^2)/(1 + 3 + 9) = 7 are both integer.
%t Select[Range[30000], Divisible[DivisorSigma[2, #1], DivisorSigma[1, #1]] && Divisible[#1, DivisorSigma[0, #1]] & ]
%Y Cf. A000005, A000203, A001157, A020487, A033950.
%K nonn,easy
%O 1,2
%A _Ilya Gutkovskiy_, Jan 01 2017
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