cp's OEIS Frontend

A386276 Numbers k such that the sequence defined by f(1) = k and f(x+1) = the sum of the three largest proper divisors of f(x), consists entirely of numbers having at least three proper divisors.

%I A386276 #12 Aug 18 2025 16:24:13
%S A386276 6,18,42,54,66,72,78,102,114,126,138,162,174,186,198,216,222,234,246,
%T A386276 258,282,294,306,318,342,354,366,378,402,414,426,438,462,474,486,498,
%U A386276 504,522,534,546,558,582,594,606,618,642,648,654,666,678,702,714,726,738
%N A386276 Numbers k such that the sequence defined by f(1) = k and f(x+1) = the sum of the three largest proper divisors of f(x), consists entirely of numbers having at least three proper divisors.
%C A386276 Numbers k of the form 6*i*12^j, where gcd(i, 10) = 1 and j >= 0.
%H A386276 Vincenzo Librandi, <a href="/A386276/b386276.txt">Table of n, a(n) for n = 1..3709</a>
%H A386276 Art of Problem Solving, <a href="https://artofproblemsolving.com/wiki/index.php/2025_IMO_Problems/Problem_4">2025 IMO Problems/Problem 4</a>
%F A386276 a(n) = 55*n/4 + O(log n). - _Charles R Greathouse IV_, Aug 18 2025
%t A386276 is[k_]:=Module[{v},v=IntegerExponent[k,2]; OddQ[v]&&Mod[k,5]!=0&&2*IntegerExponent[k,3]>v] Select[Range[1,1000],is] (* _Vincenzo Librandi_, Jul 22 2025 *)
%o A386276 (PARI) is(k) = my(v=valuation(k, 2)); v%2 && k%5 && 2*valuation(k, 3)>v;
%Y A386276 Cf. A080257.
%K A386276 nonn,easy,changed
%O A386276 1,1
%A A386276 _Jinyuan Wang_, Jul 17 2025