# [seqfan] Re: A combinatorial problem

Alois Heinz heinz at hs-heilbronn.de
Mon Aug 2 20:27:43 CEST 2010

```By "arrangements" you probably mean "permutations", see also
http://mathworld.wolfram.com/Arrangement.html

I computed different values of A179926(n) for the following n:
12, 18, 20, 28, 30, 36, 42, 44, 45

First example: A179926(12)=3:
[12, 6, 3, 1, 2, 4]
[12, 4, 2, 6, 3, 1]
[12, 4, 2, 1, 3, 6]
Last example: A179926(45)=3:
[45, 15, 5, 1, 3, 9]
[45, 9, 3, 15, 5, 1]
[45, 9, 3, 1, 5, 15]

seq (A179926(n), n=1..120);
0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2,
1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 18,
1, 1, 2, 2, 2, 8, 1, 2, 2, 4, 1, 18, 1, 3, 3,
2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 106,
1, 2, 3, 1, 2, 18, 1, 3, 2, 18, 1, 17, 1, 2,
3, 3, 2, 18, 1, 5, 1, 2, 1, 106, 2, 2, 2, 4,
1, 106, 2, 3, 2, 2, 2, 6, 1, 3, 3, 8, 1, 18,
1, 4, 18, 2, 1, 17, 1, 18, 2, 5, 1, 18, 2, 3,
3, 2, 2, 572

Alois

> Dear SeqFans,
>
> I have submitted the following sequence:
>
> %I A179926
> %S A179926 0,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,4,1,2,1,2,1,12,1,1,2,2,2,
> %T A179926 2,1,2,2,4,1,12,1,2,2,2,1
> %N A179926 a(n) is the number of arrangements of all divisors of n of the form d_1=n, d_2, d_3,...,d_tau(n) such that d_(i+1)/d_i is prime or 1/prime
> %C A179926 In view of formulas given below, there are many common first terms with A001221.
> %F A179926 a(p^k)=1, a(p*q)=a(p^2*q)=a(p^2*q^2)=2, a(p^3*q)=4, a(pqr)=12 (here p,q,r are distinct primes, k>=1).
> %Y A179926 A000005 A001221
> %K A179926 nonn
> %O A179926 1,1
>
> More terms? More formulas? Corrections?
>
> Regards,