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

Author

Logan J. Kleinwaks, Mar 24 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A270970 (similar sequence counting trivial solutions).

Programs

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 *)

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

Formula

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

Extensions

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