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A106464 Antidiagonal sums of number triangle A003989. 1
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, 45, 15, 32, 36, 24, 41, 57, 18, 27, 43, 60, 20, 66, 21, 51, 72, 33, 23, 84, 42, 60, 57, 61, 26, 81, 67, 88, 64, 42, 29, 135, 30, 45, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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]

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

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

MAPLE

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

map(f, [$0..100]); # Robert Israel, May 11 2018

MATHEMATICA

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

PROG

(PARI) a(n) = sum(k=0, n\2, gcd(n-2*k+1, k+1)); \\ Michel Marcus, May 11 2018

(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

CROSSREFS

Cf. A003989, A106466.

Sequence in context: A257241 A239964 A290585 * A093003 A118096 A296440

Adjacent sequences:  A106461 A106462 A106463 * A106465 A106466 A106467

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 03 2005

EXTENSIONS

Name corrected by R. J. Mathar, May 11 2018

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)