|
%I #25 May 13 2020 09:00:28
%S 0,0,0,0,0,12,0,24,18,40,0,120,0,84,90,160,0,270,0,260,168,220,0,672,
%T 100,312,270,616,0,1020,0,800,396,544,350,1656,0,684,546,1680,0,1932,
%U 0,1496,1260,1012,0,3168,294,1850,918,2080,0,3132,770,3136
%N 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.
%F a(n) = n*(sigma(n) - tau(n) - n + (n mod 2)) for n > 2.
%F a(p) = 0 for all primes p.
%e 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.
%o (PARI) a(n)={if(n<=2, 0, n*(sigma(n) - numdiv(n) - n + n%2))} \\ _Andrew Howroyd_, Mar 05 2020
%Y Cf. A000005 (tau), A000203 (sigma).
%K nonn
%O 1,6
%A _Brian Barsotti_, Mar 04 2020
%E Terms a(31) and beyond from _Andrew Howroyd_, Mar 05 2020
|
