A260589 - OEIS

%I #26 Nov 21 2018 00:33:27

%S 11,11,3,3,37,37,11,11,101,101,41,41,271,271,3,3,7,7,11,11,13,13,37,

%T 37,239,239,4649,4649,11,11,73,73,101,101,137,137,3,3,3,3,37,37,

%U 333667,333667,12345678910987654321,7,17636684157301569664903,3,3,7,7,2799473675762179389994681,1109,4729

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

%C 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.)

%C 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.

%H M. F. Hasler, <a href="/A260589/b260589.txt">Table of k, a(k) for k = 1..150</a> (Rows n = 2 through 30, flattened.)

%H M. F. Hasler, <a href="/wiki/User:M._F._Hasler/Work_in_progress/Factorization_of_A173426_%3D_123...321#Factorizations">Factorization of A173426 = 123...321</a>, OEIS wiki, July 2015.

%F   n |  A173426(n) | factors = n-th row of this table

%F   1 |      1      | []

%F   2 |     121     | [11, 11]

%F   3 |    12321    | [3, 3, 37, 37]

%F   4 |   1234321   | [11, 11, 101, 101]

%F   5 |  123454321  | [41, 41, 271, 271]

%F   6 | 12345654321 | [3, 3, 7, 7, 11, 11, 13, 13, 37, 37]

%o (PARI) A260589_row(n)=A027746_row(A173426(n))

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

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

%K nonn,tabf,base

%O 1,1

%A _M. F. Hasler_, Jul 29 2015