A241972 a(n) = n - A137849(n).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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 A185782

Adjacent sequences: A241969 A241970 A241971 * A241973 A241974 A241975

Keyword

nonn

Author

J. Lowell, May 03 2014

Extensions

More terms from Tom Edgar, May 03 2014

Status

approved