A394917 - OEIS

%I #21 May 18 2026 10:56:01

%S 1,2,4,6,8,16,12,18,20,28,32,64,24,30,40,42,54,56,66,70,78,88,102,104,

%T 105,110,114,128,36,100,196,225,256,48,80,112,162,176,208,272,304,368,

%U 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

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

%H Daniel Suteu, <a href="/A394917/b394917.txt">Table of n, a(n) for n = 1..13069</a> (first 20 rows)

%e Irregular triangle begins as:

%e  1;

%e  2;

%e  4;

%e  6, 8;

%e  16;

%e  12, 18, 20, 28, 32;

%e  64;

%e  24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128;

%e  36, 100, 196, 225, 256;

%e  48, 80, 112, 162, 176, 208, 272, 304, 368, 405, 464, 496, 512;

%e  1024.

%p T:= n-> select(k-> numtheory[tau](k)=n, [$1..2^(n-1)])[]:

%p seq(T(n), n=1..11);  # _Alois P. Heinz_, Apr 07 2026

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

%o (Magma) [[k: k in [1..2^(n - 1)] | #Divisors(k) eq n]: n in [1..12]];

%o (PARI) row(n) = select(x->(numdiv(x)==n), [1..2^(n - 1)]); \\ _Michel Marcus_, Apr 07 2026

%Y Cf. A000005, A000079, A001055, A008578.

%Y Column 1 gives A005179.

%Y Row lengths give A393179.

%K nonn,tabf

%O 1,2

%A _Juri-Stepan Gerasimov_, Apr 06 2026