cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A056760 Integers with exactly 2 prime divisors such that the cube of the number of divisors exceeds the number.

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%I A056760 #19 Aug 27 2025 09:15:00
%S A056760 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,48,
%T A056760 50,51,52,54,55,56,57,58,62,63,68,72,75,76,80,88,92,96,98,99,100,104,
%U A056760 108,112,116,117,124,135,136,144,147,148,152,153,160,162,164,171,172
%N A056760 Integers with exactly 2 prime divisors such that the cube of the number of divisors exceeds the number.
%C A056760 Numbers with 8 prime divisors also occur among cases satisfying relation d^3>n.
%C A056760 Prime divisors are counted without multiplicity. - _Harvey P. Dale_, May 14 2012
%H A056760 Donovan Johnson, <a href="/A056760/b056760.txt">Table of n, a(n) for n = 1..254</a> (complete sequence)
%F A056760 Integers k = (p^w)*(q^u) such that d(k)^3 > k, where d(k) = A000005(k).
%e A056760 The sequence is finite and almost surely complete. Between 270000 and 17000000 no more cases were found. The last 3 entries are: 165888, 186624, 248832. E.g. k = 1024*343 = 248832, with 66 divisors and d^3 = 287496 > 248832.
%t A056760 Select[Range[180],PrimeNu[#]==2&&DivisorSigma[0,#]^3>#&] (* _Harvey P. Dale_, May 14 2012 *)
%Y A056760 Cf. A000005, A033033-A033035, A034884.
%K A056760 fini,full,nonn,changed
%O A056760 1,1
%A A056760 _Labos Elemer_, Aug 16 2000