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A179529 Number of terms of A083207 in 12 consecutive numbers. 7
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
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-François Alcover, Apr 30 2017, after T. D. Noe *)
CROSSREFS
Sequence in context: A085297 A080972 A037814 * A118668 A273429 A273915
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 19 2010
STATUS
approved

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Last modified June 22 14:15 EDT 2024. Contains 373587 sequences. (Running on oeis4.)