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%I #14 May 17 2020 15:39:25
%S 1,3,7,15,31,42,99,119,193,218,463,340,807,682,849,1087,1939,1299,
%T 2775,1862,2615,3050,5107,2988,5681,5242,6439,5656,10615,5562,13083,
%U 9631,11367,12362,14153,10531,22719,17578,19361,16050,31243,16728,36207,24284,26133
%N a(n) is the number of sets modulo n which can be formed by a finite arithmetic sequence.
%F a(n) = sigma(n) + n*(tau(n) - 1 - 3*floor(n/2) + Sum_{i=1..floor(n/2)} n/gcd(n,i)).
%e For n = 3, the a(3) = 7 solutions are {1}; {2}; {3}; {1,2}; {1,3}; {2,3}; {1,2,3}.
%t Array[#3 + #1 (#2 - 1 - 3 #4 + Sum[#1/GCD[#1, i], {i, #4}]) & @@ Join[{#}, DivisorSigma[{0, 1}, #], {Floor[#/2]}] &, 45] (* _Michael De Vlieger_, May 04 2020 *)
%o (PARI) a(n) = {sigma(n) + n*(numdiv(n) - 1 - 3*(n\2) + sum(i=1, n\2, n/gcd(n,i)))} \\ _Andrew Howroyd_, May 03 2020
%Y Cf. A000005 (tau), A000203 (sigma).
%K nonn
%O 1,2
%A _Brian Barsotti_, May 03 2020
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