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A337209
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Triangle read by rows T(n,k), (n >= 1, k > = 1), in which row n has length A000070(n-1) and every column gives A000203, the sum of divisors function.
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16
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1, 3, 1, 4, 3, 1, 1, 7, 4, 3, 3, 1, 1, 1, 6, 7, 4, 4, 3, 3, 3, 1, 1, 1, 1, 1, 12, 6, 7, 7, 4, 4, 4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 8, 12, 6, 6, 7, 7, 7, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 8, 12, 12, 6, 6, 6, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4
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OFFSET
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1,2
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COMMENTS
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Conjecture: the sum of row n equals A066186(n), the sum of all parts of all partitions of n.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
3, 1;
4, 3, 1, 1;
7, 4, 3, 3, 1, 1, 1;
6, 7, 4, 4, 3, 3, 3, 1, 1, 1, 1, 1;
12, 6, 7, 7, 4, 4, 4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1;
8, 12, 6, 6, 7, 7, 7, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, ...
...
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MATHEMATICA
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A337209row[n_]:=Flatten[Table[ConstantArray[DivisorSigma[1, n-m], PartitionsP[m]], {m, 0, n-1}]]; Array[A337209row, 10] (* Paolo Xausa, Sep 02 2023 *)
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PROG
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(PARI) f(n) = sum(k=0, n-1, numbpart(k));
T(n, k) = {if (k > f(n), error("invalid k")); if (k==1, return (sigma(n))); my(s=0); while (k <= f(n-1), s++; n--; ); sigma(1+s); }
tabf(nn) = {for (n=1, nn, for (k=1, f(n), print1(T(n, k), ", "); ); ); } \\ Michel Marcus, Jan 13 2021
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CROSSREFS
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Sum of divisors of terms of A176206.
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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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