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A241972
a(n) = n - A137849(n).
1
0, 0, 1, 0, 3, 0, 5, 1, 4, 3, 9, 0, 11, 5, 7, 2, 15, 1, 17, 3, 11, 12, 21, 0, 16, 14, 15, 5, 27, 2, 29, 7, 20, 20, 23, 1, 35, 23, 25, 6, 39, 6, 41, 14, 22, 29, 45, 0, 35, 17, 33, 18, 51, 8, 37, 11, 38, 39, 57, 0, 59, 41, 33, 15, 45, 12, 65, 27, 47, 23
OFFSET
1,5
COMMENTS
Number of integers, m, such that 1<=m<=n and d_i(n)>d_i(m) for at least one index 1<=i<=Min(d(n),d(m)) where d_i(k) denotes the i-th smallest divisor of k and d(k) denotes the number of divisors of k.
LINKS
EXAMPLE
a(10) = 3 because A137849(10)=7. Also, there are 3 integers, 4, 6, and 8, whose divisors meet the criterion from the comment for n = 10 (the third smallest divisor of 4 is 4 and the third smallest divisor of 10 is 5; similarly 6 and 8 meet the criterion).
PROG
(Sage)
def a(n):
N=n.divisors()
count=0
for m in [1..n]:
M=m.divisors()
for i in range(min(len(N), len(M))):
if N[i]>M[i]:
count+=1
break
return count
[a(i) for i in [1..70]] # Tom Edgar, May 03 2014
CROSSREFS
Cf. A137849, A094783 (values where a(n) = 0).
Sequence in context: A086696 A259743 A247015 * A357823 A226770 A376625
KEYWORD
nonn
AUTHOR
J. Lowell, May 03 2014
EXTENSIONS
More terms from Tom Edgar, May 03 2014
STATUS
approved