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A332053
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a(n) is the number of sets modulo n which can be formed by a finite arithmetic sequence, whose complement cannot be formed by a finite arithmetic sequence.
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0
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0, 0, 0, 0, 0, 12, 0, 24, 18, 40, 0, 120, 0, 84, 90, 160, 0, 270, 0, 260, 168, 220, 0, 672, 100, 312, 270, 616, 0, 1020, 0, 800, 396, 544, 350, 1656, 0, 684, 546, 1680, 0, 1932, 0, 1496, 1260, 1012, 0, 3168, 294, 1850, 918, 2080, 0, 3132, 770, 3136
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = n*(sigma(n) - tau(n) - n + (n mod 2)) for n > 2.
a(p) = 0 for all primes p.
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EXAMPLE
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One example of such a set would be {0, 2, 4} mod 8. This set can be formed by starting with 0 and adding 2 twice. However, the set's complement, {1, 3, 5, 6, 7} mod 8, cannot be formed by any arithmetic sequence without including the original set.
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PROG
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(PARI) a(n)={if(n<=2, 0, n*(sigma(n) - numdiv(n) - n + n%2))} \\ Andrew Howroyd, Mar 05 2020
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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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