A130508 -id:A130508 - cp's OEIS frontend

A130509 a(1)=3. a(2)=1. a(3)=2. a(n+3) = 3 + a(n), for all positive integers n.

3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 30, 28, 29, 33, 31, 32, 36, 34, 35, 39, 37, 38, 42, 40, 41, 45, 43, 44, 48, 46, 47, 51, 49, 50, 54, 52, 53, 57, 55, 56, 60, 58, 59, 63, 61, 62, 66, 64, 65, 69, 67

Offset: 1

Leroy Quet, Jun 01 2007

This sequence is the inverse permutation of A130508.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A130508.

LinearRecurrence[{1, 0, 1, -1}, {3, 1, 2, 6}, 100] (* Amiram Eldar, Jan 31 2023 *)

a(n) = n - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3). - Wesley Ivan Hurt, Sep 26 2017

Sum_{n>=1} (-1)^n/a(n) = log(2)/3. - Amiram Eldar, Jan 31 2023

A366423 Multiplicative with a(p^e) = p^(e+1-p) if p|e, and p^(e+1) otherwise.

Original entry on oeis.org

1, 4, 9, 2, 25, 36, 49, 16, 27, 100, 121, 18, 169, 196, 225, 8, 289, 108, 361, 50, 441, 484, 529, 144, 125, 676, 3, 98, 841, 900, 961, 64, 1089, 1156, 1225, 54, 1369, 1444, 1521, 400, 1681, 1764, 1849, 242, 675, 2116, 2209, 72, 343, 500, 2601, 338, 2809, 12, 3025

Offset: 1

Amiram Eldar, Nov 17 2023

A permutation of the positive integers. 1 is the only fixed point.

a(n) is a powerful number (A001694) if and only if n is not in A100717.

Cf. A000040, A001694, A005117, A007947, A048102, A072873, A100717, A103889, A130508, A342090.

Similar sequences: A011262, A011264.

f[p_, e_] := p^(e + 1 + If[Mod[e, p] == 0, -p, 0]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^(f[i,2] + 1 + if(!(f[i,2]%f[i,1]), -f[i,1])));}

a(2^e) = 2^A103889(e).
a(3^e) = 3^A130508(e).
A007947(a(n)) = A007947(n).
a(A051674(n)) = A000040(n).
a(n) is squarefree (A005117) if and only if n is in A048102.
a(A048102(n)) = A007947(A048102(n)).
a(n) == 0 (mod n) if and only if n is not in A342090.
a(n) | n if and only if n is in A072873.
Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Product_{p prime} (1 - 1/p + 1/(1 + p) - (p-1)/(p^p * (1 + p^p))) = 0.660264348361... .

cp's OEIS Frontend

A130509 a(1)=3. a(2)=1. a(3)=2. a(n+3) = 3 + a(n), for all positive integers n.

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