

A126215


a(1)=1. a(n) = sum of the earlier terms, a(k) (for 1<=k<=n1), where every integer coprime to a(k) and <= a(k) is also coprime to n.


1



1, 1, 2, 4, 8, 4, 12, 32, 16, 12, 20, 28, 44, 40, 4, 228, 64, 256, 292, 76, 4, 72, 88, 328, 80, 52, 328, 48, 116, 4, 120, 2384, 4, 76, 28, 496, 184, 456, 28, 288, 908, 4, 256, 172, 124, 284, 300, 1540, 1656, 2132, 28, 2248, 428, 3196, 1572, 1684, 712, 328, 428, 424, 428
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..61.


EXAMPLE

The positive integers coprime to a(k) and <= a(k), for 1<=k<=8, are for a(1):{1}, for a(2):{1}, for a(3):{1}, for a(4):{1,3}, for a(5):{1,3,5,7}, for a(6):{1,3}, for a(7):{1,5,7,11} and for a(8):{1,3,5,7,...,29,31}.
Those terms a(k), 1<=k<=8, which don't have any integers which are not coprime to 9 among those positive integers which are <=a(k) and coprime to a(k) are the terms a(1)=1,a(2)=1,a(3)=2 and a(7)=12. So a(9) = 1+1+2+12 = 16.


MATHEMATICA

f[n_, k_] := Select[Range[k], GCD[ #, n] == 1 &]; g[l_List] := Block[{fn = f[Length[l] + 1, Max @@ l]}, Append[l, Plus @@ Select[l, Union[f[ #, # ], fn] == fn &]]]; Nest[g, {1}, 60] (* Ray Chandler, Dec 21 2006 *)


CROSSREFS

Cf. A126214.
Sequence in context: A133992 A294094 A290288 * A165617 A273170 A135447
Adjacent sequences: A126212 A126213 A126214 * A126216 A126217 A126218


KEYWORD

nonn


AUTHOR

Leroy Quet, Dec 20 2006


EXTENSIONS

Extended by Ray Chandler, Dec 21 2006


STATUS

approved



