A394917 Irregular triangle read by rows in which row n lists all k from [1..2^(n - 1)] with exactly n divisors.

1, 2, 4, 6, 8, 16, 12, 18, 20, 28, 32, 64, 24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 36, 100, 196, 225, 256, 48, 80, 112, 162, 176, 208, 272, 304, 368, 405, 464, 496, 512, 1024, 60, 72, 84, 90, 96, 108, 126, 132, 140, 150, 156, 160, 198, 200, 204, 220, 224, 228, 234, 260

Offset

1,2

Links

Daniel Suteu, Table of n, a(n) for n = 1..13069 (first 20 rows)

Example

Irregular triangle begins as:
 1;
 2;
 4;
 6, 8;
 16;
 12, 18, 20, 28, 32;
 64;
 24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128;
 36, 100, 196, 225, 256;
 48, 80, 112, 162, 176, 208, 272, 304, 368, 405, 464, 496, 512;
 1024.

Maple

T:= n-> select(k-> numtheory[tau](k)=n, [$1..2^(n-1)])[]:
seq(T(n), n=1..11);  # Alois P. Heinz, Apr 07 2026

Mathematica

row[n_] := Select[Range[2^(n-1)], DivisorSigma[0, #] == n &]; Array[row, 12] // Flatten (* Amiram Eldar, Apr 07 2026 *)

Prog

(Magma) [[k: k in [1..2^(n - 1)] | #Divisors(k) eq n]: n in [1..12]];
(PARI) row(n) = select(x->(numdiv(x)==n), [1..2^(n - 1)]); \\ Michel Marcus, Apr 07 2026

Crossrefs

Cf. A000005, A000079, A001055, A008578.

Column 1 gives A005179.

Row lengths give A393179.

Sequence in context: A192333 A068902 A269332 * A077569 A270140 A333020

Adjacent sequences: A394914 A394915 A394916 * A394918 A394919 A394920

Keyword

nonn,tabf

Author

Juri-Stepan Gerasimov, Apr 06 2026

Status

approved