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 A179527 Characteristic function of numbers in A083207. 5
 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A179528(n+1) - A179528(n); a(A083207(n)) = 1; a(A083210(n)) = 0; a(n) = A057427(A083206(n)); let n such that a(n)=1 and m coprime to n, then a(m*n)=1, this was proved by R. Gerbicz (lemma for proving A179529(n)>0). LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 Peter Luschny, Zumkeller Numbers MATHEMATICA ZumkellerQ[n_] := Module[{d = Divisors[n], t, ds, x}, ds = Total[d]; If[Mod[ds, 2] > 0, False, t = CoefficientList[Product[1 + x^i, {i, d}], x]; t[[1 + ds/2]] > 0]]; a[n_] := Boole[ZumkellerQ[n]]; Array[a, 105] (* Jean-François Alcover, Apr 30 2017, after T. D. Noe *) PROG (Other) PolyML (the leading dots are just for readability): fun A179527(n) = ... let fun ch(m, k) = ........... if k <= m .............. then ch(m, k+1) orelse (n mod k = 0 andalso ch(m-k, k+1)) .............. else (m = 0) .... in if A000203(n) mod 2 = 0 andalso ch(A000203(n) div 2 - n, 1) .......... then 1 .......... else 0 ... end; CROSSREFS Sequence in context: A324824 A025458 A286925 * A172051 A093958 A044936 Adjacent sequences:  A179524 A179525 A179526 * A179528 A179529 A179530 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jul 19 2010 STATUS approved

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Last modified March 29 01:25 EDT 2020. Contains 333104 sequences. (Running on oeis4.)