A383003 -id:A383003 - cp's OEIS frontend

A382998 a(n) = Sum_{d|n} phi(n/d) * (-n)^(d-1).

1, -1, 11, -66, 629, -7750, 117655, -2097676, 43046889, -999990036, 25937424611, -743008622708, 23298085122493, -793714765724686, 29192926025492783, -1152921504875290680, 48661191875666868497, -2185911559727680349982, 104127350297911241532859

Offset: 1

Seiichi Manyama, Apr 12 2025

sign

Main diagonal of A382993.
Main diagonal of A382995.
Cf. A000010, A382997, A383003.

a(n) = sumdiv(n, d, eulerphi(n/d)*(-n)^(d-1));

a(n) = (1/n) * A382997(n).
a(n) = Sum_{k=1..n} (-n)^(gcd(n,k) - 1).
a(n) = [x^n] Sum_{k>=1} phi(k) * log(1 + n*x^k) / k.
a(n) = [x^n] Sum_{k>=1} phi(k) * x^k / (1 + n*x^k).

A383010 a(n) = -Sum_{d|n} (-n)^d.

Original entry on oeis.org

1, -2, 30, -268, 3130, -46470, 823550, -16781368, 387421227, -9999900090, 285311670622, -8916103453380, 302875106592266, -11112006720144694, 437893890381622140, -18446744078004584688, 827240261886336764194, -39346408075098212291754, 1978419655660313589123998

Offset: 1

Seiichi Manyama, Apr 12 2025

Cf. A066108, A383003.

PARI
```
a(n) = -sumdiv(n, d, (-n)^d);
```

A383012 a(n) = Sum_{d|n} mu(n/d) * (-n)^(d-1).

Original entry on oeis.org

1, -3, 8, -60, 624, -7805, 117648, -2096640, 43046640, -1000009989, 25937424600, -743008120140, 23298085122480, -793714780783665, 29192926025339776, -1152921504338411520, 48661191875666868480, -2185911559749714602652, 104127350297911241532840

Offset: 1

Seiichi Manyama, Apr 12 2025

sign

Main diagonal of A383011.

Cf. A008683, A075147, A382998, A383003.

a(n) = sumdiv(n, d, moebius(n/d)*(-n)^(d-1));

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

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

cp's OEIS Frontend

A382998 a(n) = Sum_{d|n} phi(n/d) * (-n)^(d-1).

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PARI

Formula

A383010 a(n) = -Sum_{d|n} (-n)^d.

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Author

Keywords

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Programs

PARI

A383012 a(n) = Sum_{d|n} mu(n/d) * (-n)^(d-1).

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Author

Keywords

Crossrefs

Programs

PARI

Formula