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.

6, 18, 42, 54, 66, 72, 78, 102, 114, 126, 138, 162, 174, 186, 198, 216, 222, 234, 246, 258, 282, 294, 306, 318, 342, 354, 366, 378, 402, 414, 426, 438, 462, 474, 486, 498, 504, 522, 534, 546, 558, 582, 594, 606, 618, 642, 648, 654, 666, 678, 702, 714, 726, 738

Offset: 1

Author

Jinyuan Wang, Jul 17 2025

Keywords

• nonn
• easy
• changed

Comments

Numbers k of the form 6*i*12^j, where gcd(i, 10) = 1 and j >= 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3709
• Art of Problem Solving, 2025 IMO Problems/Problem 4

Crossrefs

Cf. A080257.

Programs

Mathematica

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 *)

PARI

is(k) = my(v=valuation(k, 2)); v%2 && k%5 && 2*valuation(k, 3)>v;

Formula

a(n) = 55*n/4 + O(log n). - Charles R Greathouse IV, Aug 18 2025