A307653 -id:A307653 - cp's OEIS frontend

A344430 a(n) = Sum_{k=1..n} mu(k) * k^k.

1, -3, -30, -30, -3155, 43501, -780042, -780042, -780042, 9999219958, -275312450653, -275312450653, -303150419042906, 10808856406515110, 448702746787374485, 448702746787374485, -826791559139549389692, -826791559139549389692

Offset: 1

Seiichi Manyama, May 19 2021

sign

Cf. A001923, A002321, A008683, A307653, A336276, A336277, A336278, A336279, A344429.

a[n_] := Sum[MoebiusMu[k] * k^k, {k,1,n}]; Array[a, 20] (* Amiram Eldar, May 19 2021 *)
Accumulate[Table[MoebiusMu[n]n^n,{n,20}]] (* Harvey P. Dale, Jan 25 2022 *)

PARI
```
a(n) = sum(k=1, n, moebius(k)*k^k);
```

from sympy import mobius
def A344430(n): return sum(mobius(k)*k**k for k in range(1,n+1)) # Chai Wah Wu, Apr 05 2023

A307654 a(n) = Product_{p|n, p prime} (1 - p^p).

Original entry on oeis.org

1, -3, -26, -3, -3124, 78, -823542, -3, -26, 9372, -285311670610, 78, -302875106592252, 2470626, 81224, -3, -827240261886336764176, 78, -1978419655660313589123978, 9372, 21412092, 855935011830, -20880467999847912034355032910566, 78, -3124, 908625319776756, -26, 2470626

Offset: 1

Seiichi Manyama, Apr 20 2019

sign

			a(6) = (1 - 2^2) * (1 - 3^3) = 78.

Seiichi Manyama, Table of n, a(n) for n = 1..388

Cf. A023900, A307653, A321222.

f[p_, e_] := 1 - p^p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 28] (* Amiram Eldar, May 13 2021 *)

cp's OEIS Frontend

A344430 a(n) = Sum_{k=1..n} mu(k) * k^k.

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