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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65593

Index entries for characteristic functions

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: A101637 A011729 A297044 * A277161 A216038 A011728

Adjacent sequences:  A296210 A296211 A296212 * A296214 A296215 A296216

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 08 2017

STATUS

approved

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Last modified August 20 03:48 EDT 2019. Contains 326139 sequences. (Running on oeis4.)