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%I #13 Jul 21 2019 06:28:09
%S 38,46,295,38,235,749,38,3687,6128,38,1415,46,38,4254,10451,38,46,
%T 8351,38,334,4511,38,3398,295,38,1286,46,38,148870,11015,38,46,35519,
%U 38,10239,14072,38,235,76088,38,5991,46,38,718,295,38,46,11654,38,30761
%N Least non-balanced x (i.e., not in A020492) such that sigma(2n-1,x)/phi(x) is an integer.
%H Amiram Eldar, <a href="/A078539/b078539.txt">Table of n, a(n) for n = 2..1200</a>
%F a(n) = min{x; sigma(1,x) mod phi(x) = 0 but sigma(2n-1, x) mod phi(x) is not 0}.
%e n=7: 2n-1 = 13, cases of sigma(13,x)/phi(x) is an integer listed in A015771: 1, 2, 3,6, 12, etc,; the first term which is non-balanced, i.e., not in A020492 is a(7) = 749 = A020492(31); increasing n, the trend of a(n) is roughly the same. If 2n-1 = 3s, i.e., is divisible by 3, then a(3s) = 38. Similar relationships hold for 2n - 1 = 5s, 7s, 11s, etc.
%t Table[fl=1; Do[s1=DivisorSigma[1, n]/EulerPhi[n]; sk=DivisorSigma[2*k-1, n]/EulerPhi[n]; If[ !IntegerQ[s1]&&IntegerQ[sk]&&Equal[fl, 1], Print[{n, 2*k-1}]; fl=0], {n, 1, 1000000}], {k, 2, 100}]
%Y Cf. A000005, A000010, A015759-A015774, A020492, A078538.
%K nonn
%O 2,1
%A _Labos Elemer_, Dec 02 2002
%E a(31) corrected by _Amiram Eldar_, Jul 21 2019
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