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A110077 a(n) is the smallest number m such that sigma(m)=10^n and if there is no such m, a(n)=0. 10
1, 0, 0, 0, 8743, 71193, 640737, 5906061, 65624979, 590624811, 5498542791, 55995364341, 549871699041, 5582882097891, 55828827410391, 542546715730761, 5469955867029591, 53226216007355979, 532262221390168479, 5300249369031696429, 52602977416561263909, 531074469279114815229 (list; graph; refs; listen; history; text; internal format)
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 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
Sequence in context: A250881 A234707 A257748 * A300566 A203377 A183361
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

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Last modified April 21 06:29 EDT 2024. Contains 371850 sequences. (Running on oeis4.)