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A072808
Smallest m such that sigma(m) mod phi(n) = n or 0 if no solution exists.
2
4, 5, 8, 24, 0, 22, 16, 21, 450, 40, 25, 48, 50, 136, 32, 110, 100, 90, 144, 88, 0, 656, 121, 102, 0, 80, 169, 96, 0, 68, 64, 55, 676, 464, 289, 65, 0, 117, 162, 91, 0, 116, 225, 85, 0, 272, 529, 95, 0, 148, 288, 133, 0, 164, 0, 115, 0, 160, 841, 147, 0, 333, 128, 247
OFFSET
1,1
COMMENTS
Warning: It is only conjectured that there are no solutions for n such that a(n) = 0. The search for solutions tested all m <= 10^10 for these n.
For odd remainders a(n) is a square or twice a square. See A028982, except terms 1 and 2.
All zeros corresponding to odd terms a(n) with n < 64 confirmed up to m <= 10^24. - Giovanni Resta, Apr 02 2020
FORMULA
a(n) = Min{x; Mod(A000203(x), A000010(x))=n} or 0 if apparently no solutions.
EXAMPLE
For n=4: a(4)=24 since sigma(24)=60, phi(24)=8 and Mod(60, 8)=4.
MATHEMATICA
f[x_] := Mod[DivisorSigma[1, x], EulerPhi[x]]; t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000000}]; t
KEYWORD
nonn,changed
AUTHOR
Labos Elemer, Jul 12 2002
EXTENSIONS
Name corrected by Sean A. Irvine, Oct 30 2024
STATUS
approved