A076191 First differences of A001222.

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

Offset: 1

Author

Joseph L. Pe, Nov 03 2002

Keywords

• easy
• sign

Comments

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

Links

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

Crossrefs

Cf. A001222, A045920.

Programs

Haskell

a076191 n = a076191_list !! (n-1)
a076191_list = zipWith (-) (tail a001222_list) a001222_list
-- Reinhard Zumkeller, Mar 20 2012

Mathematica

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

PARI

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

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

Extensions

Name changed by Arkadiusz Wesolowski, Jul 27 2012