A270875 Number of subsets of {1,...,n} with sum of elements equal to least common multiple of elements and at least two elements.

0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 6, 9, 9, 10, 13, 15, 15, 19, 19, 33, 35, 35, 35, 47, 47, 47, 50, 57, 57, 101, 101, 106, 108, 108, 108, 127, 127, 127, 128, 249, 249, 268, 268, 272, 358, 358, 358, 406, 406, 408, 409, 411, 411, 424, 424, 501, 502, 502, 502, 1190, 1190

Offset

1,6

Comments

It appears that the sequence of n for which a(n)>a(n-1) has a large overlap with A175904.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = A270970(n) - n. - Michel Marcus, Mar 27 2016

Example

For n=3, the subsets of {1,2,3} with at least two elements have (sum,LCM) as follows: {1,2}->(3,2), {1,3}->(4,3), {2,3}->(5,6), {1,2,3}->(6,6). Only the last satisfies sum=LCM, so a(3)=1.

Mathematica

Table[Length[Transpose@ {Total /@ #, LCM @@@ #} /. {a_, b_} /; a != b -> Nothing &@ Rest[Subsets[Range@ n] /. {_} -> Nothing]], {n, 2, 22}] (* Michael De Vlieger, Mar 24 2016 *)

Prog

(PARI) a(n) = {nb = 0; S = vector(n, k, k); for (i = 0, 2^n - 1, ss = vecextract(S, i); if (vecsum(ss) == lcm(ss), nb++); ); nb - n; } \\ Michel Marcus, Mar 26 2016

Crossrefs

Cf. A270970 (similar sequence counting trivial solutions).

Sequence in context: A098382 A098180 A357411 * A117752 A299775 A227191

Adjacent sequences: A270872 A270873 A270874 * A270876 A270877 A270878

Keyword

nonn

Author

Logan J. Kleinwaks, Mar 24 2016

Extensions

More terms added using A270970 by Jinyuan Wang, May 02 2020

Status

approved