A110076 a(n) is the largest number m such that sigma(m)=10^n, or if there is no such m a(n)=0.

1, 0, 0, 0, 9481, 99301, 997501, 9993001, 99948001, 999795001, 9999750001, 99998670001, 999997950001, 9999986700001, 99999975000001, 999999198750001, 9999999187500001, 99999995096707501, 999999919987500001, 9999999986700000001, 99999499999999800001, 999999999907500000001, 9999999999796009687501

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