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.

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

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