

A132273


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


5



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
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OFFSET

1,2


COMMENTS

a(n) is the sum of the terms in the nth 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..n1]) 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, nk+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



