A110077 a(n) is the smallest number m such that sigma(m)=10^n and if there is no such m, a(n)=0.

1, 0, 0, 0, 8743, 71193, 640737, 5906061, 65624979, 590624811, 5498542791, 55995364341, 549871699041, 5582882097891, 55828827410391, 542546715730761, 5469955867029591, 53226216007355979, 532262221390168479, 5300249369031696429, 52602977416561263909, 531074469279114815229

Offset: 0

Author

Farideh Firoozbakht, Aug 01 2005

Keywords

• nonn

Comments

A110078(n) gives number of solutions of the equation sigma(x)=10^n.

Conjecture: For n>3 a(n) is positive.

Examples

			a(9)=590624811 because sigma(590624811)=sigma(3^3*7*3124999) sigma(3^3)*sigma(7)*sigma(3124999)=40*8*3125000=10^9 and 590624811 is the smallest number m with this property (sigma(m)=10^9).
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..1000
• Max Alekseyev, PARI/GP scripts for miscellaneous math problems
• Max A. Alekseyev, Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2

Crossrefs

Cf. A110076, A110078.

Programs

PARI

{ a(n) = invsigma(10^n)[1] } \\ Max Alekseyev, Apr 26 2010

Extensions

a(10)-a(11) from Donovan Johnson and Farideh Firoozbakht, Nov 22 2008

a(12) onward from Max Alekseyev, Apr 26 2010, Mar 06 2014