For an integer, let denote the greatest prime factor of , i.e., the number in the factorization
with
for .
For ,
3, ..., the first few are 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, ... (OEIS A006530). The greatest multipleprime
factors for squareful integers are 2, 2, 3, 2,
2, 3, 2, 2, 5, 3, 2, 2, 3, ... (OEIS A046028).
A number for which
is called an unusual number by Greene and Knuth (1990) and a -rough numbers by Finch
(2001). The first few -rough numbers are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15,
17, 19, 20, 21, ... (OEIS A064052). The probability
that a random positive integer is -rough is (Schroeppel 1972).
A number that is not -rough is called, not surprisingly, a -smooth number (or sometimes, a "round
number"). The first few are 1, 4, 8, 9, 12, 16, 18, 24, 25, 27, ... (OEIS
A048098).
, let 
denote the greatest prime factor of 
, i.e., the number 
in the factorization
for 
.
For 
,
3, ..., the first few are 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, ... (OEIS A006530). The greatest multiple prime
factors for squareful integers are 2, 2, 3, 2,
2, 3, 2, 2, 5, 3, 2, 2, 3, ... (OEIS A046028).
is called an unusual number by Greene and Knuth (1990) and a 
-rough numbers by Finch
(2001). The first few 
-rough numbers are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15,
17, 19, 20, 21, ... (OEIS A064052). The probability
that a random positive integer is 
-rough is 
(Schroeppel 1972).
-rough is called, not surprisingly, a 
-smooth number (or sometimes, a "round
number"). The first few are 1, 4, 8, 9, 12, 16, 18, 24, 25, 27, ... (OEIS
A048098).
and 
."
Aequationes Math. 17, 211-321, 1978.Finch, S. "RE:
Unusual Numbers." 27 Aug 2001. 
." §B46 in 
." Nieuw Arch. Wisk. 1, 113-122,
1953.Schroeppel, R. Item 29 in Beeler, M.; Gosper, R. W.; and Schroeppel,
R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239,
p. 13, Feb. 1972.