|
%I #54 Nov 07 2022 12:24:03
%S 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,
%T 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,
%U 24,58,3,60,26,4,1,40,12,66,3,8,2,70,4,72,32,32,3
%N The bottom entry in the absolute difference triangle of the divisors of n.
%C Note that if n is prime then a(n) = n - 1.
%C Where records occurs gives the odd noncomposite numbers (A006005).
%C First differs from A187202 at a(14).
%C 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]
%H T. D. Noe, <a href="/A187203/b187203.txt">Table of n, a(n) for n = 1..10000</a>
%e a(18) = 4 because the divisors of 18 are 1, 2, 3, 6, 9, 18, and the absolute difference triangle of the divisors is:
%e 1 . 2 . 3 . 6 . 9 . 18
%e . 1 . 1 . 3 . 3 . 9
%e . . 0 . 2 . 0 . 6
%e . . . 2 . 2 . 6
%e . . . . 0 . 4
%e . . . . . 4
%e with bottom entry a(18) = 4.
%e Note that A187202(18) = 12.
%t Table[d = Divisors[n]; While[Length[d] > 1, d = Abs[Differences[d]]]; d[[1]], {n, 100}] (* _T. D. Noe_, Aug 01 2011 *)
%t Table[Nest[Abs[Differences[#]]&,Divisors[n],DivisorSigma[0,n]-1],{n,100}]//Flatten (* _Harvey P. Dale_, Nov 07 2022 *)
%o (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
%o (Haskell)
%o a187203 = head . head . dropWhile ((> 1) . length) . iterate diff . divs
%o where divs n = filter ((== 0) . mod n) [1..n]
%o diff xs = map abs $ zipWith (-) (tail xs) xs
%o -- _Reinhard Zumkeller_, Aug 02 2011
%Y Cf. A006005, A027750, A187202, A187205, A187208.
%K nonn
%O 1,3
%A _Omar E. Pol_, Aug 01 2011
%E Edited by _Omar E. Pol_, May 14 2016
|
