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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 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

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Last modified February 1 06:22 EST 2023. Contains 359981 sequences. (Running on oeis4.)