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A249242
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Squarefree primitive abundant numbers (using the second definition: having no abundant proper divisors, cf. A091191).
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5
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30, 42, 66, 70, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1398, 1430, 1434, 1446, 1506
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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