A062537 - OEIS

%I #29 Jul 11 2023 19:32:58

%S 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,

%T 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,

%U 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

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

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

%H Reinhard Zumkeller, <a href="/A062537/b062537.txt">Table of n, a(n) for n = 1..10000</a>

%H Jon Awbrey, <a href="/A061396/a061396a.txt">Illustrations of riffs for small integers</a>.

%H Jon Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>.

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

%F a(n) = Sum_{k=1..A001221(n)} (a(A049084(A027748(n,k))) + a(A124010(n,k)) + 1). - _Reinhard Zumkeller_, Feb 26 2013

%t 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 *)

%o (Haskell)

%o import Data.Function (on)

%o a062537 1 = 0

%o a062537 n = sum $ map (+ 1) $

%o    zipWith ((+) `on` a062537) (map a049084 $ a027748_row n) (a124010_row n)

%o -- _Reinhard Zumkeller_, Feb 26 2013

%Y Cf. A061396.

%Y Cf. A001221, A027748, A049084, A124010.

%K nonn,easy,nice

%O 1,3

%A _David W. Wilson_, Jun 25 2001