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Largest square dividing the sum of divisors of n: a(n) = A008833(sigma(n)).
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%I #10 Jul 29 2019 10:27:59

%S 1,1,4,1,1,4,4,1,1,9,4,4,1,4,4,1,9,1,4,1,16,36,4,4,1,1,4,4,1,36,16,9,

%T 16,9,16,1,1,4,4,9,1,16,4,4,1,36,16,4,1,1,36,49,9,4,36,4,16,9,4,4,1,

%U 16,4,1,4,144,4,9,16,144,36,1,1,1,4,4,16,4,16,1,121,9,4,16,36,4,4,36,9,9,16,4,64,144,4,36

%N Largest square dividing the sum of divisors of n: a(n) = A008833(sigma(n)).

%H Antti Karttunen, <a href="/A326039/b326039.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A008833(A000203(n)) = A326038(n)^2.

%F a(n) = A000203(n) - A326040(n).

%t Module[{sqs=Range[100,1,-1]^2},Table[SelectFirst[sqs,Divisible[ DivisorSigma[ 1,n],#]&],{n,100}]] (* _Harvey P. Dale_, Jul 29 2019 *)

%o (PARI)

%o A008833(n) = (n/core(n));

%o A326039(n) = A008833(sigma(n));

%Y Cf. A000203, A008833, A326038, A326040.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 05 2019