

A125728


a(n) = Sum_{k=1..n} (number of positive integers <= k which are coprime to both k and n).


2



1, 2, 4, 5, 10, 7, 18, 16, 23, 19, 42, 24, 58, 38, 46, 56, 96, 52, 120, 72, 93, 93, 172, 91, 171, 132, 176, 143, 270, 116, 308, 218, 237, 228, 280, 201, 432, 286, 330, 275, 530, 237, 584, 368, 394, 417, 696, 357, 666, 431, 570, 515, 882, 452, 716, 565, 712, 665
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OFFSET

1,2


COMMENTS

Equals row sums of triangle A144379.  Gary W. Adamson, Sep 19 2008


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = Sum_{j=1..n} Sum_{k(n*j)} mu(k) * floor(j/k), where mu(k) is the Mobius (Moebius) function and the inner sum is over the positive divisors, k, of (n*j).


EXAMPLE

The positive integers coprime to k and <= k are, as k runs from 1 to 8, 1; 1; 1, 2; 1,3; 1,2,3,4; 1,5; 1,2,3,4,5,6; 1,3,5,7. So we want, so as to get a(8), the number of 1's, 3's, 5's and 7's in this concatenated list, since the positive integers <=8 and coprime to 8 are 1,3,5,7. In the concatenated list there are eight 1's, four 3's, three 5's and one 7. So a(8) = 8 + 4 + 3 + 1 = 16.


MATHEMATICA

f[n_] := Sum[Sum[ Boole[GCD[j, k] == 1 && GCD[j, n] == 1], {j, k}], {k, n}]; Table[f[n], {n, 60}] (* Ray Chandler, Feb 03 2007 *)


CROSSREFS

Cf. A144379.  Gary W. Adamson, Sep 19 2008
Sequence in context: A122991 A245512 A232616 * A276608 A173660 A307805
Adjacent sequences: A125725 A125726 A125727 * A125729 A125730 A125731


KEYWORD

nonn


AUTHOR

Leroy Quet, Feb 02 2007


EXTENSIONS

Extended by Ray Chandler, Feb 03 2007


STATUS

approved



