cp's OEIS Frontend

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

%I A187203 #57 Aug 18 2025 00:09:34
%S A187203 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 A187203 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 A187203 24,58,3,60,26,4,1,40,12,66,3,8,2,70,4,72,32,32,3
%N A187203 The bottom entry in the absolute difference triangle of the divisors of n.
%C A187203 Note that if n is prime then a(n) = n - 1.
%C A187203 Where records occurs gives the odd noncomposite numbers (A006005).
%C A187203 First differs from A187202 at a(14).
%C A187203 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 A187203 T. D. Noe, <a href="/A187203/b187203.txt">Table of n, a(n) for n = 1..10000</a>
%e A187203 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 A187203   1 . 2 . 3 . 6 . 9 . 18
%e A187203   . 1 . 1 . 3 . 3 . 9
%e A187203   . . 0 . 2 . 0 . 6
%e A187203   . . . 2 . 2 . 6
%e A187203   . . . . 0 . 4
%e A187203   . . . . . 4
%e A187203 with bottom entry a(18) = 4.
%e A187203 Note that A187202(18) = 12.
%t A187203 Table[d = Divisors[n]; While[Length[d] > 1, d = Abs[Differences[d]]]; d[[1]], {n, 100}] (* _T. D. Noe_, Aug 01 2011 *)
%t A187203 Table[Nest[Abs[Differences[#]]&,Divisors[n],DivisorSigma[0,n]-1],{n,100}]//Flatten (* _Harvey P. Dale_, Nov 07 2022 *)
%o A187203 (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 A187203 (Haskell)
%o A187203 a187203 = head . head . dropWhile ((> 1) . length) . iterate diff . divs
%o A187203    where divs n = filter ((== 0) . mod n) [1..n]
%o A187203          diff xs = map abs $ zipWith (-) (tail xs) xs
%o A187203 -- _Reinhard Zumkeller_, Aug 02 2011
%Y A187203 Cf. A006005, A027750, A187202, A187205, A187208.
%K A187203 nonn,changed
%O A187203 1,3
%A A187203 _Omar E. Pol_, Aug 01 2011
%E A187203 Edited by _Omar E. Pol_, May 14 2016