

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
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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



