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 A337209 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. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: the sum of row n equals A066186(n), the sum of all parts of all partitions of n. LINKS Paolo Xausa, Table of n, a(n) for n = 1..10980 (rows 1..21 of the triangle, flattened) FORMULA T(n,k) = A000203(A176206(n,k)). EXAMPLE 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, ... ... MATHEMATICA A337209row[n_]:=Flatten[Table[ConstantArray[DivisorSigma[1, n-m], PartitionsP[m]], {m, 0, n-1}]]; Array[A337209row, 10] (* Paolo Xausa, Sep 02 2023 *) PROG (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 CROSSREFS Sum of divisors of terms of A176206. Cf. A339278 (another version). Cf. A000070, A000203, A066186, A221529, A238442, A339258. Sequence in context: A016573 A191818 A055171 * A101038 A064883 A090844 Adjacent sequences: A337206 A337207 A337208 * A337210 A337211 A337212 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Nov 27 2020 STATUS approved

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Last modified August 11 12:11 EDT 2024. Contains 375069 sequences. (Running on oeis4.)