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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A119674 A064920 A064916 * A057859 A242992 A029579
KEYWORD
nonn
AUTHOR
Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001
EXTENSIONS
More terms from Ralf Stephan, Jun 02 2005
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)