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References to 'number of distinct prime factors function'
1. $2^{\omega(n)} \le \tau(n) \le 2^{\Omega(n)}$ by Wkbj79
2. $\displaystyle \sum_{n \le x} y^{\omega(n)}=O_y(x(\log x)^{y-1})$ for $y \ge 0$ by Wkbj79
3. Achilles number by PrimeFan
4. additive function by Wkbj79
5. if $\mu(n) = (-1)^{\omega(n)}$ then $\tau(n) = 2^{\omega(n)}$ by 1and2and4
6. integer factorization by PrimeFan
7. Lucas-Carmichael number by PrimeFan
8. negative number by PrimeFan
9. number of (nondistinct) prime factors function by Wkbj79
10. Pratt certificate by PrimeFan
11. primary pseudoperfect number by CompositeFan
12. quasiperfect number by CompositeFan
13. Ruth-Aaron pair by CompositeFan
14. sphenic number by CompositeFan
15. table of integer factorizations for $0 < n < 1001$ by PrimeFan
16. table of values of the M\"obius function and the Mertens function by PrimeFan
17. Zeisel number by CompositeFan