A382943 Numbers k such that A382883(k) = 0.

12, 16, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189

Offset: 1

Author

Peter Luschny, Apr 12 2025

Keywords

• nonn

Comments

See the comments in A382883.

Crossrefs

Cf. A382881, A382883, A383016, A383017, A059404, A217261.

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[200], f[#] == 0 &] (* Amiram Eldar, Apr 29 2025 *)

SageMath

def A382943List(upto): return [n for n in srange(1, upto) if A382883(n) == 0]
# Or:
def isA382943(n): return n > 1 and 0 == sum(A382881(n, k) for k in srange(2, n + 1))

Formula

a = {n >= 2 | 0 = Sum_{k=2..n} A382881(n, k)}.

A382883 = a union A383016 union A383017.

Conjecture: A059404 is a subsequence.