A215285 Numbers m such that Sum_{k=1..m} (m - k | k) = phi(m), where (i|j) is the Kronecker symbol and phi(m) is the Euler totient function.

1, 2, 3, 4, 6, 9, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744

Offset: 1

Author

Peter Luschny, Aug 07 2012

Keywords

• nonn

Comments

n is in this sequence if and only if sum_{k=1..n} (n-k|k) = sum_{k=1..n} |(n-k|k)|.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000010, A215200, A215283, A215284.

Programs

Mathematica

Reap[ Do[ If[ Sum[ KroneckerSymbol[n - k, k], {k, 1, n}] == EulerPhi[n], Print[n]; Sow[n]], {n, 1, 8000}]][[2, 1]] (* Jean-François Alcover, Jul 29 2013 *)

PARI

is(m) = sum(k = 1, m, kronecker(m-k, k)) == eulerphi(m); \\ Amiram Eldar, Nov 08 2024

Sage

def A215200_row(n): return [kronecker_symbol(n-k, k) for k in (1..n)]
[n for n in (1..1000) if sum(A215200_row(n)) == euler_phi(n)]