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A076191 First differences of A001222. 5
1, 0, 1, -1, 1, -1, 2, -1, 0, -1, 2, -2, 1, 0, 2, -3, 2, -2, 2, -1, 0, -1, 3, -2, 0, 1, 0, -2, 2, -2, 4, -3, 0, 0, 2, -3, 1, 0, 2, -3, 2, -2, 2, 0, -1, -1, 4, -3, 1, -1, 1, -2, 3, -2, 2, -2, 0, -1, 3, -3, 1, 1, 3, -4, 1, -2, 2, -1, 1, -2, 4, -4, 1, 1, 0, -1, 1, -2, 4, -1, -2, -1, 3, -2, 0, 0, 2, -3, 3, -2, 1, -1, 0, 0, 4, -5, 2, 0, 1, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

a(A045920(n)) = 0. [Reinhard Zumkeller, Mar 19 2012]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Omega(n+1)-Omega(n), where Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity.

G.f.: ((1 - x)/x)*Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). - Ilya Gutkovskiy, Mar 15 2017

MATHEMATICA

Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Flatten[Append[{1}, Table[Omega[n + 1] - Omega[n], {n, 2, 100}]]]

PROG

(Haskell)

a076191 n = a076191_list !! (n-1)

a076191_list = zipWith (-) (tail a001222_list) a001222_list

-- Reinhard Zumkeller, Mar 20 2012

(PARI) a(n) = bigomega(n + 1) - bigomega(n); \\ Indranil Ghosh, Mar 15 2017

CROSSREFS

Cf. A001222.

Sequence in context: A305258 A053616 A094718 * A282318 A286971 A025861

Adjacent sequences:  A076188 A076189 A076190 * A076192 A076193 A076194

KEYWORD

easy,sign

AUTHOR

Joseph L. Pe, Nov 03 2002

EXTENSIONS

Name changed by Arkadiusz Wesolowski, Jul 27 2012

STATUS

approved

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Last modified October 17 01:09 EDT 2018. Contains 316275 sequences. (Running on oeis4.)