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A110077
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a(n) is the smallest number m such that sigma(m)=10^n and if there is no such m, a(n)=0.
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10
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1, 0, 0, 0, 8743, 71193, 640737, 5906061, 65624979, 590624811, 5498542791, 55995364341, 549871699041, 5582882097891, 55828827410391, 542546715730761, 5469955867029591, 53226216007355979, 532262221390168479, 5300249369031696429, 52602977416561263909, 531074469279114815229
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OFFSET
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0,5
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COMMENTS
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A110078(n) gives number of solutions of the equation sigma(x)=10^n.
Conjecture: For n>3 a(n) is positive.
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LINKS
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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
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EXAMPLE
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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).
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PROG
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(PARI) { a(n) = invsigma(10^n)[1] } \\ Max Alekseyev, Apr 26 2010
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CROSSREFS
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Cf. A110076, A110078.
Sequence in context: A250881 A234707 A257748 * A300566 A203377 A183361
Adjacent sequences: A110074 A110075 A110076 * A110078 A110079 A110080
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KEYWORD
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nonn
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AUTHOR
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Farideh Firoozbakht, Aug 01 2005
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EXTENSIONS
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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
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STATUS
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approved
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