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

1,6

Links

Table of n, a(n) for n=1..56.

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

Adjacent sequences: A332050 A332051 A332052 * A332054 A332055 A332056

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