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A187203 The bottom entry in the absolute difference triangle of the divisors of n. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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]

LINKS

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

EXAMPLE

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.

MATHEMATICA

Table[d = Divisors[n]; While[Length[d] > 1, d = Abs[Differences[d]]]; d[[1]], {n, 100}] (* T. D. Noe, Aug 01 2011 *)

PROG

(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

(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

CROSSREFS

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

Sequence in context: A239641 A249151 A046791 * A187202 A125131 A003958

Adjacent sequences:  A187200 A187201 A187202 * A187204 A187205 A187206

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 01 2011

EXTENSIONS

Edited by Omar E. Pol, May 14 2016

STATUS

approved

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Last modified June 25 17:47 EDT 2019. Contains 324353 sequences. (Running on oeis4.)