OFFSET
1,2
COMMENTS
For prime p, a(p) = p. - Ralf Stephan, Jun 02 2005
a(n) is the number of times n appears in A033677. - Franklin T. Adams-Watters, Nov 18 2005
Conjecture: a(n) > n/log(n) for n > 2. - Thomas Ordowski, Jan 28 2017
a(n) is the number of integers 1<=i<=n such that all divisors of i*n are either <=i or >=n. - Chai Wah Wu, Oct 13 2023
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
EXAMPLE
a(4)=3 because there are 9 unique products in the 4 X 4 multiplication table (1 2 3 4 6 8 9 12 16), which is 3 more than the 6 unique products in the 3 X 3 multiplication table (1 2 3 4 6 9).
MAPLE
MATHEMATICA
Prepend[Differences@ #, First@ #] &@ Module[{ u = {}}, Table[Length[u = Union[u, n Range@ n]], {n, 100}]] (* Michael De Vlieger, Jan 30 2017 *)
PROG
(PARI) b(n) = #setbinop((x, y)->x*y, vector(n, i, i); );
a(n) = b(n) - b(n-1); \\ Michel Marcus, Jan 28 2017
(Python)
from itertools import takewhile
from sympy import divisors
def A062854(n): return sum(1 for i in range(1, n+1) if all(d<=i for d in takewhile(lambda d:d<n, divisors(n*i)))) # Chai Wah Wu, Oct 13 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001
EXTENSIONS
More terms from Ralf Stephan, Jun 02 2005
STATUS
approved