A371238 Euler totient function applied to the binary palindromes of even length.

2, 6, 8, 20, 24, 32, 36, 84, 96, 80, 108, 96, 144, 120, 128, 324, 320, 288, 420, 336, 360, 476, 384, 512, 432, 560, 540, 504, 632, 480, 600, 1364, 960, 1344, 1296, 1536, 1440, 1296, 1584, 1296, 1772, 1512, 1280, 1760, 1440, 1980, 1800, 1600, 1800, 2016, 1536, 1872

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

William D. Banks and Igor E. Shparlinski, Average value of the Euler function on binary palindromes, Bulletin of the Polish Academy of Sciences, Mathematics, Vol. 54, No. 2 (2006), pp. 95-101; alternative link.

Formula

a(n) = A000010(A048701(n)).

(1/N(k)) * Sum_{j, A070939(A048701(j)) = 2*k} a(j) = 3 * 2^(2*k-2) * (6/Pi^2 + O((k/log(k))^(-1/4))), where N(k) = Sum_{j, A070939(A048701(j)) = 2*k} 1 (Banks and Shparlinski, 2006).

Mathematica

EulerPhi[Select[Range[5000], EvenQ[Length[(d = IntegerDigits[#, 2])]] && PalindromeQ[d] &]]

Prog

(PARI) is(n) = Vecrev(n = binary(n)) == n && !((#n)%2);
lista(kmax) = for(k = 1, kmax, if(is(k), print1(eulerphi(k), ", ")));

Crossrefs

Cf. A000010, A006995, A048701, A059956, A070939.

Sequence in context: A135616 A069553 A275826 * A143481 A093968 A064713

Adjacent sequences: A371235 A371236 A371237 * A371239 A371240 A371241

Keyword

nonn,base,easy

Author

Amiram Eldar, Mar 16 2024

Status

approved