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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
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 * A353528 A358755 A172051
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 19 2010
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)