* π (''n''), the [[Prime number theorem|Prime counting function]] - the number of [[prime number|primes]] less than or equal to a given number ''n''. We have π(1) = 0 and π(10) = 4 (the primes below 10 being 2, 3, 5, and 7).
* ''a''<sub>0</sub>(''n'') - the sum of primes dividing ''n'', sometimes called sopfr(''n''). We have ''a''<sub>0</sub>(20) = ''a''<sub>0</sub>(2<sup>2</sup> · 5) = 2 + 2+ 5 = 9. ([http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001414 SIDN A001414]).
* ''a''<sub>1</sub>(''n'') - the sum of the distinct primes dividing ''n'', sometimes called sopf(''n''). We have ''a''<sub>1</sub>(1) = 0, ''a''<sub>1</sub>(20) = 2 + 5 = 7. ([http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A008472 SIDN A008472]).
