A383105 Numbers k such that A382883(k) != A008683(k).

4, 8, 9, 25, 27, 32, 36, 49, 64, 100, 121, 125, 128, 169, 196, 216, 225, 243, 289, 343, 361, 441, 484, 529, 676, 729, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1331, 1369, 1444, 1521, 1681, 1764, 1849, 2048, 2116, 2187, 2197, 2209, 2601, 2744, 2809, 3025

Offset: 1

Author

Peter Luschny, Apr 16 2025

Keywords

• nonn

Comments

See the comments in A382883.

Crossrefs

Cf. A382883, A008683, A383018.

Programs

Mathematica

V[n_, e_] := If[e == 1, 1, IntegerExponent[n, e]]; f[n_] := f[n] = -DivisorSum[n, V[n, #] * f[#] &, # < n &]; f[1] = 1; Select[Range[3200], f[#] != MoebiusMu[#] &] (* Amiram Eldar, Apr 29 2025 *)

SageMath

print([p for p in range(1, 3100) if A382883(p) != moebius(p)])

Formula

k in a <=> Moebius(k) = 0 and abs(A382883(k)) = 1.