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 A187202 The bottom entry in the difference table of the divisors of n. 25
 1, 1, 2, 1, 4, 2, 6, 1, 4, 0, 10, 1, 12, -2, 8, 1, 16, 12, 18, -11, 8, -6, 22, -12, 16, -8, 8, -3, 28, 50, 30, 1, 8, -12, 28, -11, 36, -14, 8, -66, 40, 104, 42, 13, 24, -18, 46, -103, 36, -16, 8, 21, 52, 88, 36, 48, 8, -24, 58, -667, 60, -26, -8, 1, 40, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Note that if n is prime then a(n) = n - 1. Note that if n is a power of 2 then a(n) = 1. a(A193671(n)) > 0; a(A187204(n)) = 0; a(A193672(n)) < 0. [Reinhard Zumkeller, Aug 02 2011] First differs from A187203 at a(14). - Omar E. Pol, May 14 2016 From David A. Corneth, May 20 2016: (Start) The bottom of the difference table of the divisors of n can be expressed in terms of the divisors of n and use of Pascal's triangle. Suppose a, b, c, d and e are the divisors of n. Then the difference table is as follows (rotated for ease of reading): a . . b-a b . . . . c-2b+a . . c-b . . . . . d-3c+3b-a c . . . . d-2c+b . . . . . . e-4d+6c-4b+a . . d-c . . . . . e-3d+3c-b d . . . . e-2d+c . . e-d e From here we can see Pascal's triangle occurring. Induction can be used to show that it's the case in general. (End) LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{k=0..d-1} (-1)^k*binomial(d-1,k)*D[d-k], where D is a sorted list of the d = A000005(n) divisors of n. - N. J. A. Sloane, May 01 2016 a(2^k) = 1. EXAMPLE a(18) = 12 because the divisors of 18 are 1, 2, 3, 6, 9, 18, and the difference triangle of the divisors is: 1 . 2 . 3 . 6 . 9 . 18 . 1 . 1 . 3 . 3 . 9 . . 0 . 2 . 0 . 6 . . . 2 .-2 . 6 . . . .-4 . 8 . . . . . 12 with bottom entry a(18) = 12. Note that A187203(18) = 4. MAPLE f:=proc(n) local k, d, lis; lis:=divisors(n); d:=nops(lis); add( (-1)^k*binomial(d-1, k)*lis[d-k], k=0..d-1); end; [seq(f(n), n=1..100)]; # N. J. A. Sloane, May 01 2016 MATHEMATICA Table[d = Divisors[n]; Differences[d, Length[d] - 1][[1]], {n, 100}] (* T. D. Noe, Aug 01 2011 *) PROG (PARI) A187202(n)={ for(i=2, #n=divisors(n), n=vecextract(n, "^1")-vecextract(n, "^-1")); n[1]}  \\ M. F. Hasler, Aug 01 2011 (Haskell) a187202 = head . head . dropWhile ((> 1) . length) . iterate diff . divs    where divs n = filter ((== 0) . mod n) [1..n]          diff xs = zipWith (-) (tail xs) xs -- Reinhard Zumkeller, Aug 02 2011 CROSSREFS Cf. A000005, A007318, A027750, A187203, A273102. Sequence in context: A249151 A046791 A187203 * A125131 A003958 A326140 Adjacent sequences:  A187199 A187200 A187201 * A187203 A187204 A187205 KEYWORD easy,sign AUTHOR Omar E. Pol, Aug 01 2011 EXTENSIONS Edited by N. J. A. Sloane, May 01 2016 STATUS approved

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Last modified June 16 14:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)