A132273 a(n) = Sum{k=1..n} (k-th integer from among those positive integers that are coprime to (n+1-k)).

1, 3, 7, 12, 20, 28, 41, 52, 69, 83, 103, 122, 149, 169, 197, 222, 257, 285, 322, 355, 397, 431, 477, 514, 567, 610, 662, 708, 769, 815, 882, 935, 1000, 1056, 1123, 1182, 1267, 1326, 1404, 1471, 1554, 1628, 1712, 1790, 1882, 1958, 2057, 2137, 2240

Offset

1,2

Comments

a(n) is the sum of the terms in the n-th antidiagonal of the A126572 array. - Michel Marcus, Mar 14 2018

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

The integers coprime to 1 are 1,2,3,4,5,6,... The 5th of these is 5. The integers coprime to 2 are 1,3,5,7,9,... The 4th of these is 7. The integers coprime to 3 are 1,2,4,5,7,... The 3rd of these is 4. The integers coprime to 4 are 1,3,5,... The 2nd of these is 3. And the integers coprime to 5 are 1,2,3,4,6,... The first of these is 1. So a(5) = 5 + 7 + 4 + 3 + 1 = 20.

Mathematica

a = {}; For[n = 1, n < 50, n++, s = 0; For[k = 1, k < n + 1, k++, c = 0; i = 1; While[c < k, If[GCD[i, n + 1 - k] == 1, c++ ]; i++ ]; s = s + i - 1]; AppendTo[a, s]]; a (* Stefan Steinerberger, Nov 01 2007 *)

Prog

(Haskell)
a132273 n = sum $ zipWith (!!) coprimess (reverse [0..n-1]) where
   coprimess = map (\x -> filter ((== 1) . (gcd x)) [1..]) [1..]
-- Reinhard Zumkeller, Jul 08 2012
(PARI) cop(k, j) = {my(nbc = 0, i = 0); while (nbc != j, i++; if (gcd(i, k)==1, nbc++)); i; }
a(n) = vecsum(vector(n, k, cop(k, n-k+1))); \\ Michel Marcus, Mar 14 2018

Crossrefs

Cf. A126572, A132274, A132275.

Sequence in context: A091369 A036698 A279169 * A130050 A173256 A330285

Adjacent sequences: A132270 A132271 A132272 * A132274 A132275 A132276

Keyword

nonn

Author

Leroy Quet, Aug 16 2007

Extensions

More terms from Stefan Steinerberger, Nov 01 2007

Status

approved