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a(n) = (sum of the divisors of n)th integer from among those positive integers which are coprime to n.
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%I #9 Oct 11 2019 14:05:29

%S 1,5,5,13,7,35,9,29,19,43,13,83,15,55,44,61,19,115,21,103,55,79,25,

%T 179,38,89,59,129,31,269,33,125,79,113,69,271,39,125,89,223,43,335,45,

%U 183,146,149,49,371,66,231,113,211,55,359,98,279,125,185,61,629,63,197,181

%N a(n) = (sum of the divisors of n)th integer from among those positive integers which are coprime to n.

%e 8 = 1 + 7 is the sum of the divisors of 7. 1,2,3,4,5,6,8,9,10,11,12,13,15,16,... are the positive integers

%e which are coprime to 7. Of these integers, 9 is the 8th. So a(7) = 9.

%t f[n_] := Block[{c = DivisorSigma[1, n], k = 0}, While[c > 0, k++; While[GCD[n, k] > 1, k++ ]; c-- ]; k ]; Table[f[n], {n, 63}] (* _Ray Chandler_, Aug 29 2006 *)

%Y Cf. A122212.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 26 2006

%E Extended by _Ray Chandler_, Aug 29 2006