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A113929 Numbers k such that sigma(k) and phi(k) are both palindromes. 1

%I #44 Jun 06 2022 16:19:33

%S 1,2,3,4,5,7,2881,15456,20930,26461,26772,43262,135536,271171,2118161,

%T 2362081,2545951,2779321,4236322,6354483,12936656,28666681,221782512,

%U 253676851,259202401,259828451,276025121,276949721,437593059,472911836

%N Numbers k such that sigma(k) and phi(k) are both palindromes.

%C phi(k) = A000010(k) is the Euler totient function, while sigma(k) = A000203(k) is the sum of divisors of k.

%H David A. Corneth, <a href="/A113929/b113929.txt">Table of n, a(n) for n = 1..47</a> (terms <= 10^14 using Max Alekseyev's invphi)

%e sigma(2118161) = 2122212 and phi(2118161) = 2114112.

%t Select[Range[473*10^6],AllTrue[{DivisorSigma[1,#],EulerPhi[ #]},PalindromeQ]&] (* _Harvey P. Dale_, Aug 30 2021 *)

%o (PARI) ispal(n) = my(d=digits(n));d == Vecrev(d) \\

%o forfactored(i=1,10^10,if(ispal(eulerphi(i))&&ispal(sigma(i)),print1(i[1],", "))) \\ _Alexandru Petrescu_, Jun 03 2022

%Y Cf. A000010, A000203, A002113.

%K base,nonn

%O 1,2

%A _Giovanni Resta_, Jan 30 2006

%E a(21)-a(31) from _Donovan Johnson_, Dec 14 2009

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Last modified April 25 07:53 EDT 2024. Contains 371964 sequences. (Running on oeis4.)