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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.

%I A056763 #23 Jun 02 2024 14:33:10
%S A056763 1,2,4,6,11,24,30,60,110,137,248,399,491,801,1146,1386,1988,2525,2914,
%T A056763 3637,4081,4334,4649,4579,4305,3867,3211,2467,1730,1119,592,272,104,
%U A056763 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
%N 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.
%C A056763 a(n) = 0 for n >= 36 since A056757 is finite and its last term is 27935107200 < 2^35. - _Amiram Eldar_, Jun 02 2024
%e A056763 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.
%e A056763 Between 2^28 and 2^29, 1730 such numbers occur, so a(29) = 1730.
%t A056763 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 *)
%Y A056763 Cf. A000005, A029837, A034884, A035033-A035035, A056757-A056767.
%K A056763 nonn
%O A056763 1,2
%A A056763 _Labos Elemer_, Aug 16 2000
%E A056763 a(30)-a(32) from _Sean A. Irvine_, May 06 2022
%E A056763 More terms from _Amiram Eldar_, Jun 02 2024