von Mangoldt function matrix

von Mangoldt matrix recurrence:

=IF(OR(ROW()=1; COLUMN()=1); 1; IF(ROW()>=COLUMN(); -SUM(INDIRECT(ADDRESS(ROW()-COLUMN()+1;
COLUMN(); 4)&":"&ADDRESS(ROW()-1; COLUMN(); 4); 4)); -SUM(INDIRECT(ADDRESS(COLUMN()-ROW()+1;
ROW(); 4)&":"&ADDRESS(COLUMN()-1; ROW(); 4); 4))))

written as a European Excel spreadsheet formula to be entered in cell A1.

American version

=IF(OR(ROW()=1, COLUMN()=1), 1, IF(ROW()>=COLUMN(), -SUM(INDIRECT(ADDRESS(ROW()-COLUMN()+1,
COLUMN(), 4)&":"&ADDRESS(ROW()-1, COLUMN(), 4), 4)), -SUM(INDIRECT(ADDRESS(COLUMN()-ROW()+1,
ROW(), 4)&":"&ADDRESS(COLUMN()-1, ROW(), 4), 4))))

keywords: von Mangoldt function, Dirichlet inverse of Euler totient function, greatest common divisor.