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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 (list; graph; refs; listen; history; text; internal format)
 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 A126611 A164019 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

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Last modified May 21 15:12 EDT 2019. Contains 323444 sequences. (Running on oeis4.)