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
KEYWORD
nonn
AUTHOR
Jon Awbrey, Aug 17 2005, based on calculations by David W. Wilson
STATUS
approved