A344441 a(n) = A061020(n) + abs(A061020(n)).

2, 0, 0, 6, 0, 4, 0, 0, 14, 8, 0, 0, 0, 12, 16, 22, 0, 0, 0, 0, 24, 20, 0, 20, 42, 24, 0, 0, 0, 0, 0, 0, 40, 32, 48, 42, 0, 36, 48, 40, 0, 0, 0, 0, 0, 44, 0, 0, 86, 0, 64, 0, 0, 40, 80, 60, 72, 56, 0, 48, 0, 60, 0, 86, 96, 0, 0, 0, 88, 0, 0, 0, 0, 72, 0, 0, 120, 0, 0, 0, 122, 80, 0, 72, 128, 84, 112, 100, 0, 56, 144

Offset: 1

Author

Antti Karttunen, May 23 2021

Keywords

• nonn

Comments

a(k) = 0 for k in A026424. - David A. Corneth, May 23 2021

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A026424, A061020, A206369, A344439, A344441.

Programs

Mathematica

With[{nn = 91}, Map[# + Abs[#] &, Drop[CoefficientList[Series[Sum[LiouvilleLambda[k] k x^k/(1 - x^k), {k, 1, #}], {x, 0, #}], x], 1] &[nn]]] (* Michael De Vlieger, May 24 2021, after Jean-François Alcover at A061020 *)

PARI

A061020(n) = {my(f=factorint(n)); prod(k=1, #f[, 2], ((-f[k, 1])^(f[k, 2]+1)-1)/(-f[k, 1]-1))};
A344441(n) = { my(u=A061020(n)); (u+abs(u)); };

Formula

a(n) = A061020(n) + A206369(n) = A061020(n) + abs(A061020(n)).

a(n) = A344440(n) - A344439(n).