A187203 The bottom entry in the absolute difference triangle of the divisors of n.

1, 1, 2, 1, 4, 2, 6, 1, 4, 0, 10, 1, 12, 2, 8, 1, 16, 4, 18, 1, 8, 6, 22, 2, 16, 8, 8, 3, 28, 4, 30, 1, 8, 12, 24, 1, 36, 14, 8, 0, 40, 4, 42, 3, 20, 18, 46, 1, 36, 0, 8, 3, 52, 8, 36, 0, 8, 24, 58, 3, 60, 26, 4, 1, 40, 12, 66, 3, 8, 2, 70, 4, 72, 32, 32, 3

Offset: 1

Author

Omar E. Pol, Aug 01 2011

Keywords

• nonn
• changed

Comments

Note that if n is prime then a(n) = n - 1.

Where records occurs gives the odd noncomposite numbers (A006005).

First differs from A187202 at a(14).

It is important to note that at each step in the process, the absolute differences are taken, and not just at the end. This sequence is therefore not abs(A187202) as I mistakenly assumed at first. - Alonso del Arte, Aug 01 2011

Examples

			a(18) = 4 because the divisors of 18 are 1, 2, 3, 6, 9, 18, and the absolute difference triangle of the divisors is:
  1 . 2 . 3 . 6 . 9 . 18
  . 1 . 1 . 3 . 3 . 9
  . . 0 . 2 . 0 . 6
  . . . 2 . 2 . 6
  . . . . 0 . 4
  . . . . . 4
with bottom entry a(18) = 4.
Note that A187202(18) = 12.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006005, A027750, A187202, A187205, A187208.

Programs

Haskell

a187203 = head . head . dropWhile ((> 1) . length) . iterate diff . divs
   where divs n = filter ((== 0) . mod n) [1..n]
         diff xs = map abs $ zipWith (-) (tail xs) xs
-- Reinhard Zumkeller, Aug 02 2011

Mathematica

Table[d = Divisors[n]; While[Length[d] > 1, d = Abs[Differences[d]]]; d[[1]], {n, 100}] (* T. D. Noe, Aug 01 2011 *)
Table[Nest[Abs[Differences[#]]&,Divisors[n],DivisorSigma[0,n]-1],{n,100}]//Flatten (* Harvey P. Dale, Nov 07 2022 *)

PARI

A187203(n)={ for(i=2,#n=divisors(n), n=abs(vecextract(n,"^1")-vecextract(n,"^-1"))); n[1]}  \\ M. F. Hasler, Aug 01 2011

Extensions

Edited by Omar E. Pol, May 14 2016