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

Author

Labos Elemer, Aug 16 2000

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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 *)

Extensions

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

More terms from Amiram Eldar, Jun 02 2024