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A102716
Triangle read by rows: T(n,k) = sigma(binomial(n,k)) (0 <= k <= n), where sigma(m) is the sum of the positive divisors of m.
1
1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 12, 7, 1, 1, 6, 18, 18, 6, 1, 1, 12, 24, 42, 24, 12, 1, 1, 8, 32, 48, 48, 32, 8, 1, 1, 15, 56, 120, 144, 120, 56, 15, 1, 1, 13, 91, 224, 312, 312, 224, 91, 13, 1, 1, 18, 78, 360, 576, 728, 576, 360, 78, 18, 1, 1, 12, 72, 288, 864, 1152, 1152, 864
OFFSET
0,5
COMMENTS
Row n contains n+1 terms. Row sums yield A074801. T(2n,n) = A067819(n).
FORMULA
T(n, k) = sigma(binomial(n, k)) (0 <= k <= n).
EXAMPLE
T(6,3)=42 because the sum of the divisors of binomial(6,3)=20 is 1+2+4+5+10+20=42.
Triangle begins:
1;
1, 1;
1, 3, 1;
1, 4, 4, 1;
1, 7, 12, 7, 1;
MAPLE
with(numtheory): T:=(n, k)->sigma(binomial(n, k)): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
MATHEMATICA
Table[DivisorSigma[1, Binomial[n, k]], {n, 0, 20}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 25 2016 *)
CROSSREFS
Sequence in context: A026374 A174032 A180979 * A173076 A134510 A335322
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Feb 06 2005
STATUS
approved