A111800 Order of the rote (rooted odd tree with only exponent symmetries) for n.

1, 3, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 7, 9, 9, 9, 11, 11, 11, 9, 11, 9, 11, 9, 11, 11, 13, 11, 9, 13, 11, 13, 11, 11, 11, 13, 13, 11, 13, 11, 13, 13, 11, 13, 11, 9, 11, 13, 13, 9, 11, 15, 13, 13, 13, 11, 15, 11, 13, 13, 9, 15, 15, 11, 13, 13, 15, 13, 13, 13, 13, 13, 13, 15, 15

Offset

1,2

Comments

A061396(n) gives the number of times that 2n+1 appears in this sequence.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

J. Awbrey, Illustrations of Rotes for Small Integers

J. Awbrey, Riffs and Rotes

Formula

a(Prod(p_i^e_i)) = 1 + Sum(a(i) + a(e_i)), product over nonzero e_i in prime factorization of n.

Example

Writing prime(i)^j as i:j and using equal signs between identified nodes:
2500 = 4 * 625 = 2^2 5^4 = 1:2 3:4 has the following rote:
` ` ` ` ` ` ` `
` ` ` o-o ` o-o
` ` ` | ` ` | `
` o-o o-o o-o `
` | ` | ` | ` `
o-o ` o---o ` `
| ` ` | ` ` ` `
O=====O ` ` ` `
` ` ` ` ` ` ` `
So a(2500) = a(1:2 3:4) = a(1)+a(2)+a(3)+a(4)+1 = 1+3+5+5+1 = 15.

Maple

with(numtheory):
a:= proc(n) option remember;
      1+add(a(pi(i[1]))+a(i[2]), i=ifactors(n)[2])
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 25 2015

Mathematica

a[1] = 1; a[n_] := a[n] = 1+Sum[a[PrimePi[i[[1]] ] ] + a[i[[2]] ], {i, FactorInteger[n]}]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A109300, A109301.

Sequence in context: A086269 A057952 A175767 * A190136 A360635 A126611

Adjacent sequences: A111797 A111798 A111799 * A111801 A111802 A111803

Keyword

nonn

Author

Jon Awbrey, Aug 17 2005, based on calculations by David W. Wilson

Status

approved