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A088036 Numbers k such that k^3 - 1 is divisible by a cube other than 1.

%I A088036 #18 Sep 10 2021 10:49:11
%S A088036 9,10,17,18,19,25,28,33,37,41,46,49,55,57,64,65,73,81,82,89,91,97,100,
%T A088036 105,109,113,118,121,126,127,129,136,137,145,153,154,161,163,169,172,
%U A088036 177,181,185,190,193,199,201,208,209,217,225,226,233,235,241,244,249
%N A088036 Numbers k such that k^3 - 1 is divisible by a cube other than 1.
%H A088036 R. J. Mathar, <a href="/A088036/b088036.txt">Table of n, a(n) for n = 1..1185</a>
%p A088036 isA046099 := proc(n)
%p A088036     local p;
%p A088036     for p in ifactors(n)[2] do
%p A088036         if op(2,p) >= 3 then
%p A088036             return true;
%p A088036         end if;
%p A088036     end do:
%p A088036     false ;
%p A088036 end proc:
%p A088036 n := 1;
%p A088036 for i from 1 to 5000 do
%p A088036     if isA046099(i^3-1) then
%p A088036         printf("%d %d\n",n,i) ;
%p A088036         n := n+1;
%p A088036     end if;
%p A088036 end do: # _R. J. Mathar_, Dec 03 2015
%t A088036 n3dcQ[n_]:=Count[Divisors[n^3-1]],_?(IntegerQ[Surd[#,3]]&)>1; Select[ Range[ 2,250],n3dcQ] (* _Harvey P. Dale_, Oct 05 2017 *)
%o A088036 (Python)
%o A088036 from sympy import factorint
%o A088036 def ok(n): return max(factorint(n**3 - 1).values()) >= 3
%o A088036 print(list(filter(ok, range(1, 250)))) # _Michael S. Branicky_, Sep 10 2021
%Y A088036 Cf. A068601, A088035.
%K A088036 nonn
%O A088036 1,1
%A A088036 _Amarnath Murthy_, Sep 19 2003
%E A088036 Corrected and extended by _Ray Chandler_, Sep 23 2003
%E A088036 Definition clarified by _Harvey P. Dale_, Oct 05 2017