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A065567 T(n,m) is the sum over all m-subsets of {1,...,n} of the gcd of the subset. 2
1, 3, 1, 6, 3, 1, 10, 7, 4, 1, 15, 11, 10, 5, 1, 21, 20, 21, 15, 6, 1, 28, 26, 36, 35, 21, 7, 1, 36, 38, 60, 71, 56, 28, 8, 1, 45, 50, 90, 127, 126, 84, 36, 9, 1, 55, 67, 132, 215, 253, 210, 120, 45, 10, 1, 66, 77, 177, 335, 463, 462, 330, 165, 55, 11, 1, 78, 105, 250, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First differences of row sums equals A034738.

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

Triangle begins:

  1;

  3,1;

  6,3,1;

  10,7,4,1;

  15,11,10,5,1;

  ...

T(4,2)=7 since gcd(1,2) + gcd(1,3) + gcd(1,4) + gcd(2,3) + gcd(2,4) + gcd(3,4) = 7.

MAPLE

with(combstruct):

a065567_row := proc(n) local k, L, l, R, comb;

R := NULL;

for k from 1 to n do

   L := 0;

   comb := iterstructs(Combination(n), size=k):

   while not finished(comb) do

      l := nextstruct(comb);

      L := L + igcd(op(l));

   od;

   R := R, L;

od;

R end: # Peter Luschny, Dec 07 2010

MATHEMATICA

Table[Plus@@(GCD@@@KSubsets[Range[n], m]), {n, 16}, {m, n}]

CROSSREFS

Cf. A065568, A034738.

Sequence in context: A122432 A131110 A133093 * A100861 A131031 A130452

Adjacent sequences:  A065564 A065565 A065566 * A065568 A065569 A065570

KEYWORD

nonn,tabl

AUTHOR

Wouter Meeussen, Nov 30 2001

STATUS

approved

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)