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Numbers n such that the sum of the divisors of n is divisible by the number of divisors of n, and the sum of the squares of the divisors of n is divisible by the sum of the divisors of n.
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%I #21 Oct 21 2016 03:58:20

%S 1,20,49,169,361,500,605,961,980,1025,1369,1445,1700,1849,2645,3380,

%T 3721,4205,4352,4489,4693,5329,6241,7220,8228,8281,8405,9409,9425,

%U 10609,11045,11849,11881,12493,12500,14045,14580,14641,15125,16129,17405,17689,18785

%N Numbers n such that the sum of the divisors of n is divisible by the number of divisors of n, and the sum of the squares of the divisors of n is divisible by the sum of the divisors of n.

%C Numbers n such that A000005(n) divides A000203(n), and A000203(n) divides A001157(n).

%H Harvey P. Dale, <a href="/A277553/b277553.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 Select[Range[50000],Divisible[DivisorSigma[1,#],DivisorSigma[0,#]] && Divisible[ DivisorSigma[2,#], DivisorSigma[1,#]]&]

%Y Cf. A000005, A000203, A001157.

%Y Intersection of A003601 and A020487. See also A020486.

%K nonn

%O 1,2

%A _Harvey P. Dale_, Oct 19 2016