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URL: https://oeis.org/A386276

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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.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Jinyuan Wang, Jul 17 2025
STATUS
approved