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A111800
Order of the rote (rooted odd tree with only exponent symmetries) for n.
19
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.
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 *)
KEYWORD
nonn
AUTHOR
Jon Awbrey, Aug 17 2005, based on calculations by David W. Wilson
STATUS
approved