A049030 Sum of sigma(j) for 1<=j<10^n, where sigma(j) = A048050(j) is the sum of the proper divisors >1 of j (excluding 1 and n).
16, 3034, 320243, 32226805, 3224444759, 322465138002, 32246681892518, 3224670122682648, 322467031114802292, 32246703322412473945, 3224670334023621455211, 322467033422357645316809, 32246703342390510922780778, 3224670334240928188556405242
Offset: 1
Examples
For n = 1, the sum of sigma(j), for j < 10 is 0 + 0 + 0 + 2 + 0 + 5 + 0 + 6 + 3 = 16, so a(1) = 16.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..36 (calculated from the b-file at A049000)
- Carlos Rivera, Problem 23.- Divisors (V) Aliquot sequences, Sociable Numbers, Prime Puzzles and Problems Connection.
Formula
At a(3) = 320243, for example, take a(3) from A049000: 820741 - 500498 = 320243. Compute 500498 from 999*1000/2 = 499500, split evenly and reverse to 500499 - 1 = 500498. Add a 9 and 0 for each successive term.
a(n) = A049000(n) - 10^n * (10^n + 1) / 2 + 2 ~ (Pi^2/12 - 1/2) * 10^(2*n). - Amiram Eldar, Feb 16 2020
Extensions
More terms from Amiram Eldar, Feb 16 2020