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A339258
Triangle read by rows T(n,k), (n >= 1, k > = 1), in which row n has length A000070(n-1) and every column gives A000005, the number of divisors function.
14
1, 2, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 4, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 4, 4, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2
OFFSET
1,2
COMMENTS
Conjecture: the sum of row n equals A006128(n), the total number of parts in 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) = A000005(A176206(n,k)).
EXAMPLE
Triangle begins:
1;
2, 1;
2, 2, 1, 1;
3, 2, 2, 2, 1, 1, 1;
2, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1;
4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1;
2, 4, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, ...
...
MATHEMATICA
A339258row[n_]:=Flatten[Table[ConstantArray[DivisorSigma[0, n-m], PartitionsP[m]], {m, 0, n-1}]]; Array[A339258row, 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 (numdiv(n))); my(s=0); while (k <= f(n-1), s++; n--; ); numdiv(1+s); }
tabf(nn) = {for (n=1, nn, for (k=1, f(n), print1(T(n, k), ", "); ); print; ); } \\ Michel Marcus, Jan 13 2021
CROSSREFS
Row sums give A006128 (conjectured).
Sequence in context: A304093 A238580 A035176 * A360326 A322976 A011793
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Nov 29 2020
STATUS
approved