A007464 Shifts left under GCD-convolution with itself.

1, 1, 2, 3, 4, 6, 6, 11, 10, 18, 16, 20, 24, 26, 20, 45, 40, 38, 34, 62, 46, 54, 50, 84, 50, 102, 78, 104, 98, 90, 70, 189, 82, 130, 84, 120, 112, 130, 120, 232, 152, 234, 132, 130, 208, 282, 140, 462, 180, 210, 220, 418, 284, 334, 260, 520, 156, 334, 556

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Crossrefs

Cf. A178063 (partial sums).

Programs

Haskell

a007464 n = a007464_list !! n
a007464_list = 1 : 1 : f [1,1] where
   f xs = y : f (y:xs) where y = sum $ zipWith gcd xs $ reverse xs
-- Reinhard Zumkeller, Jan 21 2014

Maple

a:= proc(n) option remember;
      `if`(n=0, 1, add(igcd(a(i), a(n-1-i)), i=0..n-1))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Jun 22 2012

Mathematica

a[0]=1; a[1]=1; a[n_] := a[n] = Sum[GCD[a[k], a[n-k-1]], {k, 0, n-1}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 07 2012, after Alois P. Heinz *)

PARI

N=66; v=vector(N);  v[1]=1; for(n=2,N, v[n]=sum(k=1,n-1, gcd(v[k],v[n-k])) ); v  \\ Joerg Arndt, Jun 30 2013

Python

from math import gcd
A007464_list = [1, 1]
for n in range(1,10**3):
    A007464_list.append(sum(gcd(A007464_list[i],A007464_list[n-i]) for i in range(n+1)))
# Chai Wah Wu, Dec 26 2014