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

1,3

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A061396.

Cf. A001221, A027748, A049084, A124010.

Sequence in context: A276621 A111393 A323665 * A279596 A224458 A097688

Adjacent sequences: A062534 A062535 A062536 * A062538 A062539 A062540

Keyword

nonn,easy,nice

Author

David W. Wilson, Jun 25 2001

Status

approved