A249242 Squarefree primitive abundant numbers (using the second definition: having no abundant proper divisors, cf. A091191).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Cf. A071395, A295369, A298973.

Sequence in context: A328328 A302574 A087248 * A189759 A046401 A302570

Adjacent sequences: A249239 A249240 A249241 * A249243 A249244 A249245

Keyword

nonn

Author

Derek Orr, Oct 23 2014

Extensions

Definition edited by M. F. Hasler, Feb 16 2018

Status

approved