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%I #9 Dec 22 2018 12:25:12
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N a(n) = 1 if both 1+phi(k) and 1+sigma(k) are squares, 0 otherwise.
%C Characteristic function of A063532, numbers k such that phi(k) + 1 = x^2 and sigma(k) + 1 = y^2 for some x and y.
%H Antti Karttunen, <a href="/A296213/b296213.txt">Table of n, a(n) for n = 1..65593</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%e a(15) = 1 because both 1+phi(15) = 9 and 1+sigma(15) = 25 are squares.
%t Table[If[AllTrue[{Sqrt[1+EulerPhi[n]],Sqrt[1+DivisorSigma[1,n]]},IntegerQ],1,0],{n,130}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 22 2018 *)
%o (Scheme) (define (A296213 n) (* (A010052 (+ 1 (A000010 n))) (A010052 (+ 1 (A000203 n)))))
%o (define (A296213 n) (if (zero? (A010052 (+ 1 (A000010 n)))) 0 (A010052 (+ 1 (A000203 n)))))
%K nonn
%O 1
%A _Antti Karttunen_, Dec 08 2017
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