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A187203
The bottom entry in the absolute difference triangle of the divisors of n.
17
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
1,3
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]
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 *)
Table[Nest[Abs[Differences[#]]&, Divisors[n], DivisorSigma[0, n]-1], {n, 100}]//Flatten (* Harvey P. Dale, Nov 07 2022 *)
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Aug 01 2011
EXTENSIONS
Edited by Omar E. Pol, May 14 2016
STATUS
approved