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A179529 Number of terms of A083207 in 12 consecutive numbers. 6
2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = SUM(A179527(k): n <= k < n+12);

F. Buss and T. D. Noe conjectured a(n) > 0; this is correct (proof by R. Gerbicz);

a(n+1) = A179528(n+12) - A179528(n);

a(A179530(n)) = n and a(m) <> n for m < A179530(n).

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_] := Sum[Boole[ZumkellerQ[k]], {k, n, n + 11}];

Array[a, 105] (* Jean-Fran├žois Alcover, Apr 30 2017, after T. D. Noe *)

CROSSREFS

Sequence in context: A085297 A080972 A037814 * A118668 A273429 A273915

Adjacent sequences:  A179526 A179527 A179528 * A179530 A179531 A179532

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 19 2010

STATUS

approved

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Last modified April 19 01:29 EDT 2019. Contains 322237 sequences. (Running on oeis4.)