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 A078540 Least non-balanced x (i.e., not in A020492) such that sigma(p(n),x)/phi(x) is an integer, where p(n) = n-th prime. 2

%I

%S 22,38,46,295,235,749,3687,6128,1415,4254,10451,8351,334,4511,3398,

%T 1286,148870,11051,35519,10239,14072,76088,5991,718,11654,30761,7431,

%U 20993,700654,22169,5095,4198,27415,26744,14318,48368,180878,16991

%N Least non-balanced x (i.e., not in A020492) such that sigma(p(n),x)/phi(x) is an integer, where p(n) = n-th prime.

%F a(n) = min{x; A000203(x) mod A000005(x) = 0 but sigma(A000040(n), x) mod phi(x) is not 0}.

%e n=6: p(6)=13, cases of sigma(13,x)/phi(x) is an integer are listed in A015771: 1, 2, 3, 6, 12, etc.; the first term which is non-balanced, i.e., not in A020492, is a(6) = 749 = A020492(31); a(29) = 700854 and a(45) = 510759 are remarkably large.

%t Table[fl=1; Do[s1=DivisorSigma[1, n]/EulerPhi[n]; sk=DivisorSigma[Prime[k], n]/EulerPhi[n]; If[ !IntegerQ[s1]&&IntegerQ[sk]&&Equal[fl, 1], Print[{n, Prime[k]}]; fl=0], {n, 1, 1000000}], {k, 1, 100}]

%Y Cf. A000005, A000010, A000040, A015759-A015774, A020492, A078538, A078539.

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 02 2002

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Last modified July 30 07:49 EDT 2021. Contains 346348 sequences. (Running on oeis4.)