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A332053
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.
0
0, 0, 0, 0, 0, 12, 0, 24, 18, 40, 0, 120, 0, 84, 90, 160, 0, 270, 0, 320, 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
OFFSET
1,6
FORMULA
a(n) = n*(sigma(n) - tau(n) - n + (n mod 2)) for n > 2.
a(p) = 0 for all primes p.
EXAMPLE
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.
PROG
(PARI) a(n)={if(n<=2, 0, n*(sigma(n) - numdiv(n) - n + n%2))} \\ Andrew Howroyd, Mar 05 2020
CROSSREFS
Cf. A000005 (tau), A000203 (sigma).
Sequence in context: A156390 A059680 A307170 * A225951 A333577 A278711
KEYWORD
nonn
AUTHOR
Brian Barsotti, Mar 04 2020
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Mar 05 2020
a(20) corrected by Georg Fischer, Oct 06 2024
STATUS
approved