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A062854
First differences of A027424.
13
1, 2, 3, 3, 5, 4, 7, 5, 6, 6, 11, 6, 13, 8, 9, 8, 17, 9, 19, 10, 12, 12, 23, 10, 16, 14, 15, 13, 29, 12, 31, 15, 18, 18, 20, 13, 37, 20, 21, 16, 41, 17, 43, 20, 21, 24, 47, 17, 31, 22, 27, 23, 53, 22, 31, 22, 30, 30, 59, 19, 61, 32, 28, 26, 36, 26, 67, 30, 36, 26, 71, 23, 73, 38
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
A062854 := proc(n)
A027424(n)-A027424(n-1) ;
end proc:
seq(A062854(n), n=1..40) ; # R. J. Mathar, Oct 02 2020
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