A344441 -id:A344441 - 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).

A344440 a(n) = n + A061020(n).

Original entry on oeis.org

2, 1, 1, 7, 1, 8, 1, 3, 16, 14, 1, 6, 1, 20, 23, 27, 1, 11, 1, 8, 33, 32, 1, 34, 46, 38, 7, 10, 1, 22, 1, 11, 53, 50, 59, 57, 1, 56, 63, 60, 1, 30, 1, 14, 17, 68, 1, 26, 92, 29, 83, 16, 1, 74, 95, 86, 93, 86, 1, 84, 1, 92, 21, 107, 113, 46, 1, 20, 113, 46, 1, 37, 1, 110, 33, 22, 137, 54, 1, 36, 142, 122, 1, 120, 149

Offset: 1

Antti Karttunen, May 23 2021

Compare the scatter plot to that of A061020.

Antti Karttunen, Table of n, a(n) for n = 1..12427
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A061020, A344439, A344441.

With[{nn = 85}, MapIndexed[First[#2] + #1 &, 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))}; \\ From A061020
A344440(n) = (n+A061020(n));

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

a(n) = A344439(n) + A344441(n).

cp's OEIS Frontend

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

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