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A294025
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Odd abundant numbers with a record small gap to the next odd abundant number.
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4
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OFFSET
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1,1
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COMMENTS
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The corresponding gaps are 630, 420, 210, 180, 90, 30, 18, 6.
The upper ends are 1575, 5775, 5985, 6615, 8505, 34155, 1828845, 3321765915, ...
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
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LINKS
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EXAMPLE
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Odd abundant numbers are 945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, ...
Their differences are 630, 630, 630, 630, 630, 630, 630, 420, 210, 450, 180, ...
The records of small differences are 630, 420, 210, 180, ...
And the corresponding terms are 945, 5355, 5775, 6435, ...
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,fini,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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