OFFSET
1,1
COMMENTS
If k > 3 is a term of A243128 then 4*k is a term.
The least odd term is (3/2)*prime(17)# = 2884140525231318958605.
The least term that is coprime to 6 is (5/6)*prime(1245)# = 5.629...*10^4361.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 2, 26, 287, 2725, 27660, 275298, 2754638, 27556849, 275538900, 2755151247, ... . Apparently, the asymptotic density of this sequence exists and equals 0.02755... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
60 = 2^2 * 15 is a term since it is nonsquarefree, its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15, 30} and their sum is 72 > 60.
MATHEMATICA
q[n_] := AnyTrue[(f = FactorInteger[n])[[;; , 2]], # > 1 &] && Times @@ (1 + f[[;; , 1]]) > n; Select[Range[2, 2000], q]
PROG
(PARI) is(n) = {my(f = factor(n)); if(n == 1 || vecmax(f[, 2]) == 1, return(0)); prod(i=1, #f~, f[i, 1]+1) > n};
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 09 2022
STATUS
approved