

A270875


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


1



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
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OFFSET

1,6


COMMENTS

It appears that the sequence of n for which a(n)>a(n1) 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: A051732 A098382 A098180 * 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



