

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
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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 Alekseyev, Table of n, a(n) for n = 0..1000
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

Cf. A110077, A110078.
Sequence in context: A235734 A235515 A161726 * A204722 A204961 A237104
Adjacent sequences: A110073 A110074 A110075 * A110077 A110078 A110079


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



