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%I #22 May 08 2020 07:39:44
%S 15015,19635,21945,25935,33495,1752135,1915095,1915305,119104635,
%T 134877405
%N Odd unitary abundant numbers with a record small gap to the next odd unitary abundant number.
%C The corresponding gaps are 4620, 2310, 1260, 630, 420, 330, 210, 180, 120, 30.
%C The upper ends are 19635, 21945, 23205, 26565, 33915, 1752465, 1915305, 1915485, 119104755, 134877435, ...
%C The unitary version of A294025.
%C No more terms below 10^9.
%C 10^13 < a(11) <= 42229304608764255 (gap 18), while t = 220730839027951785 and t+6 are a pair with gap 6. - _Giovanni Resta_, May 07 2020
%e Odd unitary abundant numbers are 15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, ...
%e Their differences are 4620, 2310, 1260, 2730, 630, 4830, 2100, 420, ...
%e The records of small differences are 4620, 2310, 1260, 630, 420, ...
%e And the corresponding terms are 15015, 19635, 21945, 25935, 33495, ...
%t 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
%o (PARI) usig(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
%o isok(n) = (n%2) && (usig(n) > 2*n);
%o 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
%Y Cf. A129485, A294025.
%K nonn,fini,more
%O 1,1
%A _Amiram Eldar_, Oct 22 2017
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