A355026 Irregular table read by rows: the n-th row gives the possible values of the number of divisors of numbers with n prime divisors (counted with multiplicity).

1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 6, 10, 12, 16, 18, 24, 32, 7, 12, 15, 16, 20, 24, 27, 32, 36, 48, 64, 8, 14, 18, 20, 24, 30, 32, 36, 40, 48, 54, 64, 72, 96, 128, 9, 16, 21, 24, 25, 28, 36, 40, 45, 48, 60, 64, 72, 80, 81, 96, 108, 128, 144, 192, 256

Offset

0,2

Comments

First differs from A074139 at the 8th row.

The n-th row begins with n+1, which corresponds to powers of primes, and ends with 2^n, which corresponds to squarefree numbers.

The n-th row contains the distinct values of the n-th row of A238963.

Links

Table of n, a(n) for n=0..65.

Example

Table begins:
  1;
  2;
  3, 4;
  4, 6, 8;
  5, 8, 9, 12, 16;
  6, 10, 12, 16, 18, 24, 32;
  7, 12, 15, 16, 20, 24, 27, 32, 36, 48, 64;
  8, 14, 18, 20, 24, 30, 32, 36, 40, 48, 54, 64, 72, 96, 128;
  ...
Numbers k with Omega(k) = 2 are either of the form p^2 with p prime, or of the form p1*p2 with p1 and p2 being distinct primes. The corresponding numbers of divisors are 3 and 4, respectively. Therefore the second row is {3, 4}.

Mathematica

row[n_] := Union[Times @@ (# + 1) & /@ IntegerPartitions[n]]; Array[row, 9, 0] // Flatten

Prog

(PARI) row(n) = { my (m=Map()); forpart(p=n, mapput(m, prod(k=1, #p, 1+p[k]), 0)); Vec(m) } \\ Rémy Sigrist, Jun 17 2022

Crossrefs

Cf. A000005, A001222, A036035, A063008, A074139, A238963, A355027 (row lengths).

Sequence in context: A325682 A241088 A074139 * A238963 A342940 A331527

Adjacent sequences: A355023 A355024 A355025 * A355027 A355028 A355029

Keyword

nonn,tabf

Author

Amiram Eldar, Jun 16 2022

Status

approved