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%I #22 Nov 26 2017 05:41:17
%S 945,5355,5775,6435,8415,34125,1828827,3321765909
%N Odd abundant numbers with a record small gap to the next odd abundant number.
%C The corresponding gaps are 630, 420, 210, 180, 90, 30, 18, 6.
%C The upper ends are 1575, 5775, 5985, 6615, 8505, 34155, 1828845, 3321765915, ...
%C _Emmanuel Vantieghem_ has determined that for k = 76728582876430878992529528245373 the numbers k and k+2 are abundant, so the last term of this sequence is <= k. - _Giovanni Resta_, Nov 09 2017
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_880.htm">Puzzle 880. Consecutive odd abundant integers</a>
%e Odd abundant numbers are 945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, ...
%e Their differences are 630, 630, 630, 630, 630, 630, 630, 420, 210, 450, 180, ...
%e The records of small differences are 630, 420, 210, 180, ...
%e And the corresponding terms are 945, 5355, 5775, 6435, ...
%t oaQ[n_] := OddQ[n] && DivisorSigma[1,n] > 2 n; s = Select[Range[100000], oaQ]; a={}; dmin = 1000; Do[d=s[[j+1]]-s[[j]]; If[d<dmin,AppendTo[a,s[[j]]];dmin=d],{j,1,Length[s]-1}]; a
%o (PARI) lista(nn) = {lastoa = 0; mg = oo; forstep (n=1, nn, 2, if (sigma(n) > 2*n, if (! lastoa, lastoa = n, if ((nmg = n - lastoa) < mg, mg = nmg; print1(lastoa, ", "))); lastoa = n;););} \\ _Michel Marcus_, Nov 09 2017
%Y Cf. A005231.
%K nonn,fini,more
%O 1,1
%A _Amiram Eldar_, Oct 22 2017
%E a(8) from _Giovanni Resta_, Nov 09 2017