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%I #30 Jul 14 2016 00:20:17
%S 2,5,9,11,16,17,21,23,25,26,29,33,35,37,39,41,45,47,49,50,51,53,55,58,
%T 59,61,65,67,69,71,73,77,79,81,82,83,85,87,88,89,91,95,99,100,101,103,
%U 107,109,111,113,115,116,117,119,125,129,131,136,137,141,143,145,146,147,149,155,157,159
%N Numbers not in the range of the sum of deficient divisors function.
%C Numbers which do not appear in A187793 or in A274829; that is, there is no integer N whose sum of deficient divisors is equal to a(n) for any n.
%H Donovan Johnson, <a href="/A210510/b210510.txt">Table of n, a(n) for n = 1..10000</a>
%t sdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &]; ric[n_, lap_] := Block[{s, m, p = NextPrime@lap}, m = n*p; While[(s = sdef@m) <= Lim, T[[s]] = 1; ric[m, p]; m *= p; While[(s = sdef@m) <= Lim, T[[s]] = 1; ric[m, p]; m *= p]; p = NextPrime@p; m = n*p]]; seqTo[n_] := (Lim = n; T = 0 Range[n]; T[[1]] = 1; ric[1, 1]; Flatten@Position[T, 0]); seqTo[159] (* _Giovanni Resta_, Feb 20 2013 *)
%o (PARI) v=vector(10^7); for(i=1, 10^7, if(sigma(i)<i+i, v[i]=1)); m=vector(1799); for(i=1, 10^7, d=divisors(i); s=1; for(j=2, numdiv(i), if(v[d[j]]==1, s=s+d[j])); if(s<=1799, m[s]=1)); c=0; for(i=1, 1799, if(m[i]==0, c++; write("b210510.txt", c " " i))) /* _Donovan Johnson_, Feb 20 2013 */
%Y Cf. A005100, A187793, A274829 (complement).
%K nonn
%O 1,1
%A _Timothy L. Tiffin_, Jan 25 2013
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