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A249242
Squarefree primitive abundant numbers (using the second definition: having no abundant proper divisors, cf. A091191).
5
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
OFFSET
1,1
COMMENTS
Primitive numbers in A087248.
Squarefree numbers in A091191.
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
LINKS
MATHEMATICA
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 *)
PROG
(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)))))
CROSSREFS
Intersection of A087248 and A091191.
Sequence in context: A328328 A302574 A087248 * A189759 A046401 A302570
KEYWORD
nonn
AUTHOR
Derek Orr, Oct 23 2014
EXTENSIONS
Definition edited by M. F. Hasler, Feb 16 2018
STATUS
approved