A345037 -id:A345037 - cp's OEIS frontend

A345036 a(n) = Sum_{k=1..n} (-n)^(floor(n/k) - 1).

1, -1, 11, -66, 623, -7743, 117695, -2097676, 43046069, -999989915, 25937439347, -743008621122, 23298084749141, -793714765727191, 29192926036832303, -1152921504875220776, 48661191875256608663, -2185911559727678466189, 104127350297928222613599

Offset: 1

Seiichi Manyama, Jun 06 2021

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Seiichi Manyama, Table of n, a(n) for n = 1..387

Diagonal of A345033.

Cf. A344820, A345030, A345037.

a[n_] := Sum[(-n)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 06 2021 *)

PARI
```
a(n) = sum(k=1, n, (-n)^(n\k-1));
```

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + n*x^k).

A345107 a(n) = Sum_{k=1..n} (-k)^(n - floor(n/k)).

Original entry on oeis.org

1, -1, 14, -86, 955, -11851, 183800, -3273914, 67643293, -1571615577, 40838683608, -1170198385960, 36717193651461, -1251181160936837, 46033142685018824, -1818354391006060750, 76762360864947676457, -3448789505696369210193

Offset: 1

Seiichi Manyama, Jun 08 2021

sign

Seiichi Manyama, Table of n, a(n) for n = 1..387

Cf. A345037, A345106.

a[n_] := Sum[(-k)^(n - Floor[n/k]), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 08 2021 *)

PARI
```
a(n) = sum(k=1, n, (-k)^(n-n\k));
```

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (-k)^(k-1)*x^k*(1-(-k*x)^k)/((1-(-k)^(k-1)*x^k)*(1+k*x))))

G.f.: Sum_{k>=1} (-k)^(k-1)*x^k * (1 - (-k*x)^k)/((1 - (-k)^(k-1)*x^k) * (1 + k*x)).

cp's OEIS Frontend

A345036 a(n) = Sum_{k=1..n} (-n)^(floor(n/k) - 1).

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A345107 a(n) = Sum_{k=1..n} (-k)^(n - floor(n/k)).

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Author

Keywords

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Crossrefs

Programs

Mathematica

PARI

PARI

Formula