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A294026
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Odd unitary abundant numbers with a record small gap to the next odd unitary abundant number.
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0
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OFFSET
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1,1
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COMMENTS
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The corresponding gaps are 4620, 2310, 1260, 630, 420, 330, 210, 180, 120, 30.
The upper ends are 19635, 21945, 23205, 26565, 33915, 1752465, 1915305, 1915485, 119104755, 134877435, ...
No more terms below 10^9.
10^13 < a(11) <= 42229304608764255 (gap 18), while t = 220730839027951785 and t+6 are a pair with gap 6. - Giovanni Resta, May 07 2020
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LINKS
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EXAMPLE
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Odd unitary abundant numbers are 15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, ...
Their differences are 4620, 2310, 1260, 2730, 630, 4830, 2100, 420, ...
The records of small differences are 4620, 2310, 1260, 630, 420, ...
And the corresponding terms are 15015, 19635, 21945, 25935, 33495, ...
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MATHEMATICA
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usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; ouaQ[n_] := OddQ[n] && usigma[n] > 2 n; s = Select[Range[100000], ouaQ]; a={}; dmin = 5000; 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) usig(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
isok(n) = (n%2) && (usig(n) > 2*n);
lista(nn) = {last = 0; gap = oo; forstep(n=1, nn, 2, if (isok(n), if (last, if (n - last < gap, print1(last, ", "); gap = n - last)); last = n; ); ); } \\ Michel Marcus, Dec 15 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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STATUS
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approved
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