A260587 -id:A260587 - cp's OEIS frontend

A260588 Number of prime factors, counted with multiplicity, of A173426(n) = concatenation of (1, 2, ..., n, n-1, ..., 1).

0, 2, 4, 4, 4, 10, 4, 8, 8, 1, 2, 5, 3, 6, 7, 4, 5, 8, 6, 2, 6, 3, 4, 9, 2, 6, 11, 2, 4, 10, 4, 9, 8, 6, 6, 12, 3, 6, 8, 4, 6, 7, 3, 6

Offset: 1

M. F. Hasler, Jul 29 2015

			a(2) = 2 since A173426(2) = 121 = 11*11 has twice the factor 11.
a(21) = 6 since A173426(21) = 3 * 3 * 7 * 828703 * 94364768151913037621 * 250591098443370396365457961250972909.

FactorDB, (121*10^(4*n-19) - 1002*10^(4*n-28) - 2*10^(2*n-9) + 879*10^10 + 121)/99^2.

See A260587 for the variant where only distinct prime factors are counted.
See also A075023 and A075024 for the smallest and largest prime factor of the terms.
Cf. A001222.

PARI
```
a(n)=bigomega(A173426(n))
```

a(n) = A001222(A173426(n)).

Terms beyond a(30) via factorization results by Serge Batalov, added by M. F. Hasler, Jul 30 2015

a(38)-a(44) added using factordb.com by Jinyuan Wang, Mar 05 2020

A260589 Irregular table read by rows: n-th row lists the prime factors of A173426(n), with repetition.

Original entry on oeis.org

11, 11, 3, 3, 37, 37, 11, 11, 101, 101, 41, 41, 271, 271, 3, 3, 7, 7, 11, 11, 13, 13, 37, 37, 239, 239, 4649, 4649, 11, 11, 73, 73, 101, 101, 137, 137, 3, 3, 3, 3, 37, 37, 333667, 333667, 12345678910987654321, 7, 17636684157301569664903, 3, 3, 7, 7, 2799473675762179389994681, 1109, 4729

Offset: 1

M. F. Hasler, Jul 29 2015

Row lengths are given by A260588(n). In particular, row n = 1 would have length 0, i.e., no element, because A173426(1) = 1 has no prime factors. Therefore the sequence can be considered to start with row n = 2. (The offset refers to the k-th element of the "flattened" sequence.)

For n = 1 through n = 9, A173426(n) is the square of the repunit 1...1 of length n, therefore every prime factor appears twice. This is no longer the case for n > 9.

M. F. Hasler, Table of k, a(k) for k = 1..150 (Rows n = 2 through 30, flattened.)
M. F. Hasler, Factorization of A173426 = 123...321, OEIS wiki, July 2015.

Cf. A001222, A075023, A075024, A173426, A260587, A260588.

PARI
```
A260589_row(n)=A027746_row(A173426(n))
```

vector(30,n,A027746_row(A173426(n))) \\ You may concat() this.

  n |  A173426(n) | factors = n-th row of this table
|      1      | []
|     121     | [11, 11]
|    12321    | [3, 3, 37, 37]
|   1234321   | [11, 11, 101, 101]
|  123454321  | [41, 41, 271, 271]
| 12345654321 | [3, 3, 7, 7, 11, 11, 13, 13, 37, 37]

cp's OEIS Frontend

A260588 Number of prime factors, counted with multiplicity, of A173426(n) = concatenation of (1, 2, ..., n, n-1, ..., 1).

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A260589 Irregular table read by rows: n-th row lists the prime factors of A173426(n), with repetition.

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Author

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Programs

PARI

PARI

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