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A056458
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Number of primitive (aperiodic) palindromes using a maximum of two different symbols.
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6
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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
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OFFSET
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1,1
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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a(n) = Sum_{d|n} mu(d)*A016116(1 + n/d).
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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