OFFSET
1,1
COMMENTS
First differs from its subsequence A391430 at n = 24.
Subsequence of A321147 and first differs from it at n = 20: A321147(20) = 2930852925 = (3 * 5 * 7 * 11)^2 * 13^3 is not cubefree.
If k and m are coprime terms, then k*m is also a term.
In particular, if k is a term, and m is an odd squarefree number coprime to k, then k*m is also a term. The primitive terms in this sequence (A391430) are the powerful (A001694) terms.
The asymptotic density of this sequence is (4/Pi^2) * Sum_{n>=1} 1/A064987(A112643(n)) = Sum_{n>=1} f(A391430(n)) = 5.16838... * 10^(-9), where f(n) = (4/(Pi^2*n)) * Product_{prime p|n} (p/(p+1)) if n is odd and 0 otherwise.
The least term that is not divisible by 5 is a(2572337) = 497704286448369.
The least term that is not divisible by 3 is a(5.774..*10^12) = 1117347505588495206025.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
seq[lim_] := Module[{s = Select[Range[1, Sqrt[lim], 2], SquareFreeQ[#] && DivisorSigma[-1, #] > 2 &], m, t, v = {}}, If[Length[s] > 0, m = Floor[lim/s[[1]]^2]; t = Select[Range[3, m, 2], SquareFreeQ]; v = s^2; Do[v = Join[v, s[[i]]^2 * Select[t, # <= Floor[lim/s[[i]]^2] && CoprimeQ[s[[i]], #] &]], {i, 1, Length[s]}]]; Sort[v]]; seq[3*10^9]
PROG
(PARI) isok(k) = if(k < 2 || !(k % 2), 0, my(f = factor(k)); vecmax(f[ , 2]) < 3 && prod(i = 1, #f~, sumdiv(f[i, 2], d, f[i, 1]^d)) > 2*k);
CROSSREFS
A391430 is a subsequence.
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 09 2025
STATUS
approved