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, 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

Author

Brian Barsotti, Mar 04 2020

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000005 (tau), A000203 (sigma).

Programs

PARI

a(n)={if(n<=2, 0, n*(sigma(n) - numdiv(n) - n + n%2))} \\ Andrew Howroyd, Mar 05 2020

Formula

a(n) = n*(sigma(n) - tau(n) - n + (n mod 2)) for n > 2.

a(p) = 0 for all primes p.

Extensions

Terms a(31) and beyond from Andrew Howroyd, Mar 05 2020

a(20) corrected by Georg Fischer, Oct 06 2024