A253174 For a permutation of the positive integers B={b(k)}, denote L_B(n) = Sum_{k=1..n} lambda(b(k)), where lambda(n) is Liouville's function (A008836). In this sequence, a(n) = L_B(n) in case B = A098550.
1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 9, 8, 7, 6, 7, 6, 7, 8, 9, 8, 7, 6, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 9, 10, 11, 10, 9, 10, 11, 12, 13, 14, 13, 14, 13, 12, 13, 12, 11, 10, 11, 10, 9, 8, 9, 10, 9, 8, 9, 10, 11, 12, 11, 10, 9, 10, 11, 12, 13, 12
Offset: 1
Keywords
Links
- Peter J. C. Moses, Table of n, a(n) for n = 1..1000
- M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3 (1980), 187-189.
- Eric Weisstein's World of Mathematics, Liouville Function
Programs
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Mathematica
(* b = A098550 *) b[n_ /; n <= 3] := n; b[n_] := b[n] = For[bb = Table[b[j], {j, 1, n-1}]; k=4, True, k++, If[FreeQ[bb, k] && !CoprimeQ[k, b[n-2]] && CoprimeQ[k, b[n-1]], Return[k]]]; a[1]=1; a[n_] := a[n] = a[n-1] + LiouvilleLambda[b[n]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 13 2015 *)
Formula
a(n+1) - a(n) = lambda(A098550(n+1)).
Comments