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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A080257.

Sequence in context: A163983 A191829 A023620 * A074837 A286308 A015942

Adjacent sequences: A386273 A386274 A386275 * A386277 A386278 A386279

Keyword

nonn,easy

Author

Jinyuan Wang, Jul 17 2025

Status

approved