A383124 a(n) = Sum_{d|n} A382883(d)*(n/d).

1, 1, 2, 3, 4, 2, 6, 7, 7, 4, 10, 7, 12, 6, 8, 14, 16, 8, 18, 13, 12, 10, 22, 17, 21, 12, 22, 19, 28, 8, 30, 29, 20, 16, 24, 24, 36, 18, 24, 31, 40, 12, 42, 31, 29, 22, 46, 34, 43, 22, 32, 37, 52, 26, 40, 45, 36, 28, 58, 31, 60, 30, 43, 57, 48, 20, 66, 49, 44

Offset

1,3

Comments

See the comments in A382883.

Links

Table of n, a(n) for n=1..69.

Maple

a := n -> local d; add(A382883(d)*(n/d), d in NumberTheory:-Divisors(n)):
seq(a(n), n = 1..69);

Mathematica

V[n_, e_] := If[e == 1, 1, IntegerExponent[n, e]]; f[n_] := f[n] = -DivisorSum[n, V[n, #] * f[#] &, # < n &]; f[1] = 1; a[n_] := DivisorSum[n, f[#] * n/# &]; Array[a, 100] (* Amiram Eldar, Apr 29 2025 *)

Prog

(SageMath)  # See A383104 for the function A382883Transform.
def a(n) -> int: return A382883Transform(n, lambda x: x)
print([a(n) for n in srange(1, 70)])

Crossrefs

Cf. A382883, A383104, A000010, A047994, A152958.

Sequence in context: A308085 A178970 A172054 * A354985 A344005 A375126

Adjacent sequences: A383121 A383122 A383123 * A383125 A383126 A383127

Keyword

nonn

Author

Peter Luschny, Apr 17 2025

Status

approved