login
A296213
a(n) = 1 if both 1+phi(k) and 1+sigma(k) are squares, 0 otherwise.
2
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, 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, 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
OFFSET
1
COMMENTS
Characteristic function of A063532, numbers k such that phi(k) + 1 = x^2 and sigma(k) + 1 = y^2 for some x and y.
EXAMPLE
a(15) = 1 because both 1+phi(15) = 9 and 1+sigma(15) = 25 are squares.
MATHEMATICA
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 *)
PROG
(Scheme) (define (A296213 n) (* (A010052 (+ 1 (A000010 n))) (A010052 (+ 1 (A000203 n)))))
(define (A296213 n) (if (zero? (A010052 (+ 1 (A000010 n)))) 0 (A010052 (+ 1 (A000203 n)))))
CROSSREFS
Sequence in context: A337380 A011729 A297044 * A353479 A360111 A359162
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 08 2017
STATUS
approved