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A249263 Primitive, odd, squarefree abundant numbers.

%I A249263 #46 Sep 26 2019 21:14:04
%S A249263 15015,19635,21945,23205,25935,26565,31395,33495,33915,35805,39585,
%T A249263 41055,42315,42735,45885,47355,49665,50505,51765,54285,55965,58695,
%U A249263 61215,64155,68145,70455,72345,77385,80535,82005,83265,84315,91245,95865,102795,112035,116655,118965
%N A249263 Primitive, odd, squarefree abundant numbers.
%C A249263 The subsequence of primitive terms (not multiples of smaller terms) of A112643.
%C A249263 The subsequence of squarefree terms of A006038.
%C A249263 The subsequence of odd terms of A249242.
%C A249263 Not the same as A129485. Does not contain, for example, 195195, 255255, 285285, 333795, 345345, 373065, which are in A129485. - _R. J. Mathar_, Nov 09 2014
%C A249263 Sequences A287590, A188342 and A287581 list the number, smallest* and largest of all squarefree odd primitive abundant numbers with n prime factors. (*At least whenever A188342(n) is squarefree, which appears to be the case for all n >= 5.) - _M. F. Hasler_, May 29 2017
%H A249263 Giovanni Resta, <a href="/A249263/b249263.txt">Table of n, a(n) for n = 1..10000</a>
%p A249263 # see A112643 and A006038 for the coding of isA112643 and isA006038
%p A249263 isA249263 := proc(n)
%p A249263     isA112643(n) and isA006038(n) ;
%p A249263 end proc:
%p A249263 for n from 1 do
%p A249263     if isA249263(n) then
%p A249263         print(n);
%p A249263     end if;
%p A249263 end do: # _R. J. Mathar_, Nov 10 2014
%t A249263 PrimAbunQ[n_] := Module[{x, y},
%t A249263    y = Most[Divisors[n]]; x = DivisorSigma[1, y];
%t A249263    DivisorSigma[1, n] > 2 n  &&  AllTrue[x/y, # <= 2  &]];
%t A249263 Select[Range[1, 120000, 2], PrimAbunQ[#] &&
%t A249263 AllTrue[FactorInteger[#][[All, 2]], # == 1 &]  &] (* _Robert Price_, Sep 26 2019 *)
%o A249263 (PARI) v=[]; for(k=1, 10^5, n=2*k+1; if(issquarefree(n) && sigma(n)>2*n, for(i=1, #v, n%v[i] || next(2)); print1(n, ", "); v=concat(v, n))) \\ Improved (from 20 sec to 0.2 sec) by _M. F. Hasler_, May 27 2017
%Y A249263 Intersection of A112643 and A006038.
%Y A249263 Cf. A249242, A129485.
%Y A249263 Cf. A188342 (least with n factors), A287581 (largest with n factors), A287590 (number of terms with n factors).
%K A249263 nonn
%O A249263 1,1
%A A249263 _Derek Orr_, Oct 23 2014