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

1,2

Links

Table of n, a(n) for n=1..45.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A275532 A212315 A043729 * A137170 A222813 A304078

Adjacent sequences: A331500 A331501 A331502 * A331504 A331505 A331506

Keyword

nonn

Author

Brian Barsotti, May 03 2020

Status

approved