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A110076 a(n) is the largest number m such that sigma(m)=10^n, or if there is no such m a(n)=0. 4
1, 0, 0, 0, 9481, 99301, 997501, 9993001, 99948001, 999795001, 9999750001, 99998670001, 999997950001, 9999986700001, 99999975000001, 999999198750001, 9999999187500001, 99999995096707501, 999999919987500001, 9999999986700000001, 99999499999999800001, 999999999907500000001, 9999999999796009687501 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Conjecture: For n>3 a(n) is positive.
For 4 <= n <= 102, a(n) is the product of two distinct primes, but a(103) = a(49)*a(54) and is the product of four distinct primes: 1862645149230957031249999 * 5368709119999999999999999 * 79999999999999999999999999 * 12499999999999999999999999999. - David Wasserman, Nov 18 2008
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(12)=999997950001 because sigma(999997950001)=sigma(799999*1249999) =800000*1250000=10^12 and 999997950001 is the largest number with this property(sigma(m)=10^12).
MATHEMATICA
a[0] = 1; a[1] = a[2] = a[3] = 0; a[n_] := (For[m = 1, DivisorSigma[ 1, 10^n - m] != 10^n, m++ ]; 10^n - m); Do[Print[a[n]], {n, 0, 12}]
CROSSREFS
Sequence in context: A235734 A235515 A161726 * A204722 A204961 A237104
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Jul 31 2005
EXTENSIONS
More terms from David Wasserman, Nov 18 2008
Terms a(19) onward from Max Alekseyev, Mar 06 2014
STATUS
approved

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Last modified April 19 13:40 EDT 2024. Contains 371792 sequences. (Running on oeis4.)