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A240698
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Partial sums of divisors of n, cf. A027750.
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11
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1, 1, 3, 1, 4, 1, 3, 7, 1, 6, 1, 3, 6, 12, 1, 8, 1, 3, 7, 15, 1, 4, 13, 1, 3, 8, 18, 1, 12, 1, 3, 6, 10, 16, 28, 1, 14, 1, 3, 10, 24, 1, 4, 9, 24, 1, 3, 7, 15, 31, 1, 18, 1, 3, 6, 12, 21, 39, 1, 20, 1, 3, 7, 12, 22, 42, 1, 4, 11, 32, 1, 3, 14, 36, 1, 24, 1
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OFFSET
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1,3
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COMMENTS
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Triangle read by rows in which row n lists the partial sums of divisors of n. - Omar E. Pol, Apr 12 2014
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LINKS
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FORMULA
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T(n,1) = 1, T(n,k) = T(n,k-1) + A027750(n,k), 1 < k <= n.
T(n,1) = 1;
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EXAMPLE
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. ----+------------------------+---------------------
. 1 | 1 | 1
. 2 | 1, 3 | 1, 2
. 3 | 1, 4 | 1, 3
. 4 | 1, 3, 7 | 1, 2, 4
. 5 | 1, 6 | 1, 5
. 6 | 1, 3, 6, 12 | 1, 2, 3, 6
. 7 | 1, 8 | 1, 7
. 8 | 1, 3, 7, 15 | 1, 2, 4, 8
. 9 | 1, 4, 13 | 1, 3, 9
. 10 | 1, 3, 8, 18 | 1, 2, 5, 10
. 11 | 1, 12 | 1, 11
. 12 | 1, 3, 6, 10, 16, 28 | 1, 2, 3, 4, 6, 12
. 13 | 1, 14 | 1, 13 .
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MATHEMATICA
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Table[Accumulate[Divisors[n]], {n, 30}]//Flatten (* Harvey P. Dale, Dec 30 2019 *)
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PROG
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(Haskell)
a240698 n k = a240698_tabf !! (n-1) !! (k-1)
a240698_row n = a240698_tabf !! (n-1)
a240698_tabf = map (scanl1 (+)) a027750_tabf
(PARI) row(n) = my(d=divisors(n)); vector(#d, k, sum(i=1, k, d[i])); \\ Michel Marcus, Jan 24 2022
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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