A056458 Number of primitive (aperiodic) palindromes using a maximum of two different symbols.

2, 0, 2, 2, 6, 4, 14, 12, 28, 24, 62, 54, 126, 112, 246, 240, 510, 476, 1022, 990, 2030, 1984, 4094, 4020, 8184, 8064, 16352, 16254, 32766, 32484, 65534, 65280, 131006, 130560, 262122, 261576, 524286, 523264, 1048446, 1047540, 2097150, 2094988, 4194302, 4192254

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..6610

M. R. Nester, Mathematical investigations of some plant interaction designs, PhD Thesis, (1999), University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Formula

a(n) = Sum_{d|n} mu(d)*A016116(1 + n/d).

a(n) = 2 * A056476(n). - Alois P. Heinz, Feb 18 2025

Maple

f:= proc(n) local d; add(numtheory:-mobius(d)*2^floor((1+n/d)/2), d = numtheory:-divisors(n)) end proc:
map(f, [$1..50]); # Robert Israel, Feb 18 2025

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)*2^((1 + n/d)\2)); \\ Michel Marcus, Apr 24 2020
(Python)
from sympy import mobius, divisors
def A056458(n): return sum(mobius(n//d)<<(1+d>>1) for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 18 2024

Crossrefs

Cf. A016116, A056476.

Column 2 of A284823.

Sequence in context: A183034 A354101 A078052 * A322509 A284570 A256847

Adjacent sequences: A056455 A056456 A056457 * A056459 A056460 A056461

Keyword

nonn,changed

Author

Marks R. Nester

Extensions

More terms from Michel Marcus, Apr 24 2020

Status

approved