A108504 Number of divisors of A025487(n) that are at most sqrt(A025487(n)).

1, 1, 2, 2, 2, 3, 3, 4, 4, 3, 5, 5, 6, 4, 6, 6, 8, 4, 8, 9, 7, 8, 8, 10, 5, 9, 12, 8, 12, 10, 12, 5, 11, 15, 9, 16, 12, 14, 14, 6, 16, 12, 18, 13, 18, 10, 20, 14, 18, 16, 6, 20, 14, 16, 24, 15, 21, 11, 24, 16, 23, 18, 7, 24, 15, 24, 30, 18, 24, 24, 12, 27, 25, 28, 18, 27, 32, 20, 18, 7

Offset

1,3

Links

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

Formula

a(n) = A038548(A025487(n)).

Prog

(Python)
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log, primorial, divisor_count
from oeis_sequences.OEISsequences import bisection
def A108504(n):
    if n == 1: return 1
    @lru_cache(maxsize=None)
    def g(x, m, j): return sum(g(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m-1 else max(0, x.bit_length()-j)
    def f(x):
        c = n-1+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= g(x, k, 1)
        return c
    return divisor_count(bisection(f, n, n))+1>>1 # Chai Wah Wu, Mar 24 2026

Crossrefs

Cf. A025487, A038548.

Sequence in context: A153847 A332246 A096036 * A036468 A334051 A390257

Adjacent sequences: A108501 A108502 A108503 * A108505 A108506 A108507

Keyword

nonn

Author

Christian G. Bower, Jun 06 2005

Extensions

Offset corrected by Charles R Greathouse IV, Sep 28 2012

Status

approved