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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

Index entries for characteristic functions

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-Fran├žois 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.)