A062537 Nodes in riff (rooted index-functional forest) for n.

0, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 3, 4, 4, 4, 5, 5, 5, 4, 5, 4, 5, 4, 5, 5, 6, 5, 4, 6, 5, 6, 5, 5, 5, 6, 6, 5, 6, 5, 6, 6, 5, 6, 5, 4, 5, 6, 6, 4, 5, 7, 6, 6, 6, 5, 7, 5, 6, 6, 4, 7, 7, 5, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 4, 6, 5, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 6, 5, 5, 7, 6, 6, 7, 5, 7, 8

Offset: 1

Author

David W. Wilson, Jun 25 2001

Keywords

• nonn
• easy
• nice

Comments

A061396(n) is the number of times n appears in this sequence.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Jon Awbrey, Illustrations of riffs for small integers.
• Jon Awbrey, Riffs and Rotes.

Crossrefs

Cf. A061396.

Cf. A001221, A027748, A049084, A124010.

Programs

Haskell

import Data.Function (on)
a062537 1 = 0
a062537 n = sum $ map (+ 1) $
   zipWith ((+) `on` a062537) (map a049084 $ a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Feb 26 2013

Mathematica

a[1] = 0; a[n_] := a[n] = Sum[{p, e} = pe; a[PrimePi[p]] + a[e] + 1, {pe, FactorInteger[n]}]; Array[a, 105] (* Jean-François Alcover, Jul 26 2019 *)

Formula

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

a(n) = Sum_{k=1..A001221(n)} (a(A049084(A027748(n,k))) + a(A124010(n,k)) + 1). - Reinhard Zumkeller, Feb 26 2013