A215285 - OEIS

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

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OFFSET

1,2

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

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 *)

PROG

(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)]

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

CROSSREFS

Cf. A000010, A215200, A215283, A215284.

Sequence in context: A256774 A213682 A103481 * A375621 A275173 A295394

Adjacent sequences: A215282 A215283 A215284 * A215286 A215287 A215288

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 07 2012

STATUS

approved