A179527 - OEIS

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A179527

Characteristic function of numbers in A083207.

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-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: A286925 A378598 A378540 * A353528 A358755 A172051

Adjacent sequences: A179524 A179525 A179526 * A179528 A179529 A179530

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 19 2010

STATUS

approved