A331503 a(n) is the number of sets modulo n which can be formed by a finite arithmetic sequence.

1, 3, 7, 15, 31, 42, 99, 119, 193, 218, 463, 340, 807, 682, 849, 1087, 1939, 1299, 2775, 1862, 2615, 3050, 5107, 2988, 5681, 5242, 6439, 5656, 10615, 5562, 13083, 9631, 11367, 12362, 14153, 10531, 22719, 17578, 19361, 16050, 31243, 16728, 36207, 24284, 26133

Offset: 1

Author

Brian Barsotti, May 03 2020

Keywords

• nonn

Examples

			For n = 3, the a(3) = 7 solutions are {1}; {2}; {3}; {1,2}; {1,3}; {2,3}; {1,2,3}.
		

Crossrefs

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

Programs

Mathematica

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 *)

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

Formula

a(n) = sigma(n) + n*(tau(n) - 1 - 3*floor(n/2) + Sum_{i=1..floor(n/2)} n/gcd(n,i)).