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

Author

Derek Orr, Oct 23 2014

Keywords

• nonn

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

Crossrefs

Intersection of A087248 and A091191.

Cf. A071395, A295369, A298973.

Programs

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 *)

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)))))

Extensions

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