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.

22, 38, 46, 295, 235, 749, 3687, 6128, 1415, 4254, 10451, 8351, 334, 4511, 3398, 1286, 148870, 11051, 35519, 10239, 14072, 76088, 5991, 718, 11654, 30761, 7431, 20993, 700654, 22169, 5095, 4198, 27415, 26744, 14318, 48368, 180878, 16991

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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.

Mathematica

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}]

Crossrefs

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

Sequence in context: A335373 A337460 A063252 * A057836 A078612 A039373

Adjacent sequences: A078537 A078538 A078539 * A078541 A078542 A078543

Keyword

nonn

Author

Labos Elemer, Dec 02 2002

Status

approved