A056763 Number of integers in the range (2^(n-1), 2^n] for which d(k)^3 > k holds, i.e., the cube of the number of divisors of k exceeds the number k.

1, 2, 4, 6, 11, 24, 30, 60, 110, 137, 248, 399, 491, 801, 1146, 1386, 1988, 2525, 2914, 3637, 4081, 4334, 4649, 4579, 4305, 3867, 3211, 2467, 1730, 1119, 592, 272, 104, 28, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

a(n) = 0 for n >= 36 since A056757 is finite and its last term is 27935107200 < 2^35. - Amiram Eldar, Jun 02 2024

Links

Table of n, a(n) for n=1..64.

Example

a(5) = 11 because 11 integers, {18,20,21,22,24,25,26,27,28,30,32} occur between 1+2^4 = 17 and 2^5 = 32 for which the cube of number of divisors exceeds the number itself.
Between 2^28 and 2^29, 1730 such numbers occur, so a(29) = 1730.

Mathematica

With[{s = Import["https://oeis.org/A056757/b056757.txt", "Table"][[;; , 2]]}, a[n_] := Count[s, _?(2^(n-1) < # <= 2^n &)]; Table[a[n], {n, 1, 35}]] (* Amiram Eldar, Jun 02 2024 *)

Crossrefs

Cf. A000005, A029837, A034884, A035033-A035035, A056757-A056767.

Sequence in context: A084353 A084979 A049914 * A190071 A189498 A129567

Adjacent sequences: A056760 A056761 A056762 * A056764 A056765 A056766

Keyword

nonn

Author

Labos Elemer, Aug 16 2000

Extensions

a(30)-a(32) from Sean A. Irvine, May 06 2022

More terms from Amiram Eldar, Jun 02 2024

Status

approved