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%I #25 Jun 26 2019 05:40:48
%S 30,42,66,70,78,102,114,138,174,186,222,246,258,282,318,354,366,402,
%T 426,438,474,498,534,582,606,618,642,654,678,762,786,822,834,894,906,
%U 942,978,1002,1038,1074,1086,1146,1158,1182,1194,1266,1338,1362,1374,1398,1430,1434,1446,1506
%N Squarefree primitive abundant numbers (using the second definition: having no abundant proper divisors, cf. A091191).
%C Primitive numbers in A087248.
%C Squarefree numbers in A091191.
%C According to the definition of A091191, all terms of the form 6*p, p > 3, are in this sequence (and similarly for other perfect numbers). Primitive abundant can also be defined as "having only deficient proper divisors", cf. A071395. The corresponding squarefree terms are listed in A298973, and those with n prime factors are counted in A295369. (The preceding remark shows that this count would be infinite for n = 3, using the definition of A091191.) - _M. F. Hasler_, Feb 16 2018
%H Amiram Eldar, <a href="/A249242/b249242.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range@1506, SquareFreeQ[#] && DivisorSigma[1, #] > 2 # && Times @@ Boole@ Map[DivisorSigma[1, #] <= 2 # &, Most@ Divisors@ #] == 1 &] (* _Amiram Eldar_, Jun 26 2019 after _Michael De Vlieger_ at A091191 *)
%o (PARI) v=[];for(n=1,10^5,d=0;for(j=2,ceil(sqrt(n)),if(n%(j^2),d++));if(d==ceil(sqrt(n))-1,if(sigma(n)>2*n,c=0;for(i=1,#v,if(n%v[i],c++));if(c==#v,print1(n,", ");v=concat(v,n)))))
%Y Intersection of A087248 and A091191.
%Y Cf. A071395, A295369, A298973.
%K nonn
%O 1,1
%A _Derek Orr_, Oct 23 2014
%E Definition edited by _M. F. Hasler_, Feb 16 2018