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A106464 Antidiagonal sums of number triangle A003989. 1

%I

%S 1,1,2,3,3,4,6,6,5,11,6,9,15,12,8,18,9,21,22,15,11,32,20,18,27,31,14,

%T 45,15,32,36,24,41,57,18,27,43,60,20,66,21,51,72,33,23,84,42,60,57,61,

%U 26,81,67,88,64,42,29,135,30,45,105

%N Antidiagonal sums of number triangle A003989.

%C Consider the triangle T(n, k) = A003989(n, k) = gcd(n-k+1, k), n >= 1, k = 1..n. Then a(n) = Sum_{k=0..floor(n/2)} T(n-k+1, k+1), for n >= 0. - _R. J. Mathar_, May 11 2018 [adjusted to the definition of A003989. - _Wolfdieter Lang_, May 12 2018]

%H Robert Israel, <a href="/A106464/b106464.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=0..floor(n/2)} gcd(n-2*k+1, k+1)}. [corrected by _R. J. Mathar_, May 11 2018]

%p f:= n -> add(igcd(n-2*k+1,k+1),k=0..n/2):

%p map(f, [$0..100]); # _Robert Israel_, May 11 2018

%t Array[Sum[GCD[# - 2 k + 1, k + 1], {k, 0, Floor[#/2]}] &, 61, 0] (* _Michael De Vlieger_, May 14 2018 *)

%o (PARI) a(n) = sum(k=0, n\2, gcd(n-2*k+1, k+1)); \\ _Michel Marcus_, May 11 2018

%o (GAP) Flat(List([0..70],n->Sum([0..Int(n/2)],k->Gcd(n-2*k+1,k+1)))); # _Muniru A Asiru_, May 15 2018

%Y Cf. A003989, A106466.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 03 2005

%E Name corrected by _R. J. Mathar_, May 11 2018

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Last modified April 20 02:06 EDT 2019. Contains 322291 sequences. (Running on oeis4.)