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A240951
Maximum number of dividing subsets of a set of n natural numbers.
2
1, 2, 5, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
OFFSET
1,2
COMMENTS
Let A be a set of positive integers and B a subset of A. B is said to divide A if the sum of elements in B divides the sum of elements in A.
FORMULA
a(n) = 2^(n-1) = A000079(n-1) if n>4.
From Stefano Spezia, May 03 2023: (Start)
O.g.f.: x*(1 + x^2 - 2*x^3)/(1 - 2*x).
E.g.f.: (x^3 + 3*exp(2*x) - 3)/6. (End)
EXAMPLE
n = 3: only A={k,2k,3k}, where k is a natural number, has 5 dividing subsets.
n = 4: {1, 2, 3, 6} has 8 dividing subsets: {1}, {2}, {3}, {6}, {1, 2}, {1, 3}, {1, 2, 3}, {1, 2, 3, 6}. (Corrected by Stan Wagon, Nov 07 2015)
MATHEMATICA
Join[{1, 2, 5}, NestList[2#&, 8, 40]] (* Harvey P. Dale, Sep 19 2021 *)
PROG
(PARI) a(n)=if(n==3, 5, 2^(n-1)) \\ Charles R Greathouse IV, Nov 06 2015
CROSSREFS
Cf. A000079.
Sequence in context: A048139 A357239 A071085 * A280373 A324612 A243189
KEYWORD
nonn,easy
AUTHOR
Sebastian Raba, Aug 04 2014
STATUS
approved