A344440 -id:A344440 - cp's OEIS frontend

A344439 a(n) = n - A206369(n).

0, 1, 1, 1, 1, 4, 1, 3, 2, 6, 1, 6, 1, 8, 7, 5, 1, 11, 1, 8, 9, 12, 1, 14, 4, 14, 7, 10, 1, 22, 1, 11, 13, 18, 11, 15, 1, 20, 15, 20, 1, 30, 1, 14, 17, 24, 1, 26, 6, 29, 19, 16, 1, 34, 15, 26, 21, 30, 1, 36, 1, 32, 21, 21, 17, 46, 1, 20, 25, 46, 1, 37, 1, 38, 33, 22, 17, 54, 1, 36, 20, 42, 1, 48, 21, 44, 31, 38, 1, 62

Offset: 1

Antti Karttunen, May 23 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A206369, A344440, A344441.

Array[# - # DivisorSum[#, LiouvilleLambda[#]/# &] &, 90] (* Michael De Vlieger, May 24 2021, after Enrique Pérez Herrero at A206369 *)

A206369(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ From A206369
A344439(n) = (n-A206369(n));

a(n) = n - A206369(n).

a(n) = A344440(n) - A344441(n).

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

Original entry on oeis.org

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

Antti Karttunen, May 23 2021

nonn

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

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

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

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 *)

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)); };

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

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

cp's OEIS Frontend

A344439 a(n) = n - A206369(n).

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