

A078539


Least nonbalanced x (i.e., not in A020492) such that sigma(2n1,x)/phi(x) is an integer.


11



38, 46, 295, 38, 235, 749, 38, 3687, 6128, 38, 1415, 46, 38, 4254, 10451, 38, 46, 8351, 38, 334, 4511, 38, 3398, 295, 38, 1286, 46, 38, 148870, 11015, 38, 46, 35519, 38, 10239, 14072, 38, 235, 76088, 38, 5991, 46, 38, 718, 295, 38, 46, 11654, 38, 30761
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OFFSET

2,1


LINKS

Amiram Eldar, Table of n, a(n) for n = 2..1200


FORMULA

a(n) = min{x; sigma(1,x) mod phi(x) = 0 but sigma(2n1, x) mod phi(x) is not 0}.


EXAMPLE

n=7: 2n1 = 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 nonbalanced, i.e., not in A020492 is a(7) = 749 = A020492(31); increasing n, the trend of a(n) is roughly the same. If 2n1 = 3s, i.e., is divisible by 3, then a(3s) = 38. Similar relationships hold for 2n  1 = 5s, 7s, 11s, etc.


MATHEMATICA

Table[fl=1; Do[s1=DivisorSigma[1, n]/EulerPhi[n]; sk=DivisorSigma[2*k1, n]/EulerPhi[n]; If[ !IntegerQ[s1]&&IntegerQ[sk]&&Equal[fl, 1], Print[{n, 2*k1}]; fl=0], {n, 1, 1000000}], {k, 2, 100}]


CROSSREFS

Cf. A000005, A000010, A015759A015774, A020492, A078538.
Sequence in context: A295491 A133123 A177222 * A282813 A125970 A026047
Adjacent sequences: A078536 A078537 A078538 * A078540 A078541 A078542


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 02 2002


EXTENSIONS

a(31) corrected by Amiram Eldar, Jul 21 2019


STATUS

approved



