A075767 Least m such that A(m) = -10^n, where A(n) = sigma(n) - 2n, the abundance of n.

1, 11, 101, 5090, 40028, 182525, 2000006, 44244716, 400000028, 4000000028, 2210000389844, 200000000006, 2157894737114, 160003470403376, 1600000000000496, 17702403243841424, 473046821886215264, 200000000000000006, 2000000000000000006, 320000285058337899104, 1600000010865322611056, 4027615922173870449524

Offset

0,2

Comments

For n in A049054, a(n) <= 2 * (10^n + 3); for n in A088274, a(n) <= 4 * (10^n + 7); for n in A107083, a(n) <= 16 * (10^n + 31); for n in A135115, a(n) <= 32 * (10^n + 63). - Max Alekseyev, Nov 12 2025

Links

Table of n, a(n) for n=0..21.

Jason Earls, Some Smarandache-type sequences and problems concerning abundant and deficient numbers, Smarandache Notions Journal 14:1 (2004), 265-270.

Example

a(1) = A101223(1) = 11.

Mathematica

A[m_] := DivisorSigma[1, m]-2*m; Do[m = 1; While[A[m] != -10^n, m++ ]; Print[m], {n, 0, 9}] (* Ryan Propper, Oct 01 2006 *)

Crossrefs

Cf. A049054, A088274, A101223, A107083, A135115, A292557, A292558, A363285.

Sequence in context: A233432 A052075 A070854 * A292014 A080176 A064490

Adjacent sequences: A075764 A075765 A075766 * A075768 A075769 A075770

Keyword

nonn

Author

Jason Earls, Oct 09 2002

Extensions

More terms from Ryan Propper, Oct 01 2006

a(10)-a(13) from Hiroaki Yamanouchi, Aug 24 2018

a(14)-a(18) from Max Alekseyev, Nov 12 2025

a(19)-a(21) from Max Alekseyev, Mar 09 2026

Status

approved