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

0,5

Comments

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

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

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

Example

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).

Prog

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

Crossrefs

Cf. A110076, A110078.

Sequence in context: A250881 A234707 A257748 * A300566 A203377 A183361

Adjacent sequences: A110074 A110075 A110076 * A110078 A110079 A110080

Keyword

nonn

Author

Farideh Firoozbakht, Aug 01 2005

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

Status

approved