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(2n-1, x) mod phi(x) is not 0}.
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 02 2002
EXTENSIONS
a(31) corrected by Amiram Eldar, Jul 21 2019
STATUS
approved