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 A333518 a(n) = A000720(A006530(A334468(n))). 0
 1, 2, 1, 2, 3, 1, 2, 2, 2, 3, 1, 2, 3, 3, 2, 2, 3, 4, 1, 4, 2, 3, 3, 2, 3, 2, 3, 4, 2, 3, 3, 1, 3, 4, 2, 3, 3, 2, 4, 4, 3, 4, 2, 3, 4, 2, 4, 3, 6, 3, 2, 3, 1, 3, 4, 2, 4, 3, 5, 6, 4, 3, 2, 4, 4, 4, 3, 7, 3, 4, 2, 4, 3, 3, 6, 4, 6, 2, 4, 4, 3, 5, 6, 8, 7, 3, 2, 5, 3, 4, 1, 4, 5, 3, 5, 4, 4, 2, 4, 5, 3, 5, 6, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Indices of the greatest prime factor of A334468(n). Consider A334468, a list of numbers m = n+j such that j > 0 is also the smallest number such that n+j has no prime factor > j for some n and j = A217287(n). Since prime q always contributes a novel prime divisor (i.e., q itself) to the set of distinct primes that divide at least 1 number i the range n + i (1 <= i <= j), the numbers m in A334468 are composite, and given the above, m is a product of relatively small prime factors. LINKS EXAMPLE Start with n = 1, the empty product. Incrementing n and storing the distinct prime factors each time, we encounter 2, which does not divide any previous number n. Therefore we proceed to n = 3, which is prime and its distinct prime divisor again does not divide any previous number. Finally, at 4, we have the distinct prime divisor 2, since 2 divides the product of the previous range {1, 2, 3}, we end the chain. Therefore 4 is the first term of this sequence. We list row n of A217438 below, starting with n aligned in columns: 1 2 3 2 3 3 4 5 4 5 6 7 5 6 7 6 7 7 8 9 10 11 8 9 10 11 9 10 11 10 11 12 13 14 11 12 13 14 15 12 13 14 15 13 14 15 14 15 ... Adding 1 to the last numbers seen in all the rows, we generate the sequence A334468: {4, 6, 8, 12, 15, 16, ...}. Of these, we have greatest prime factors {2, 3, 2, 3, 5, 2, ...} with indices {1, 2, 1, 2, 3, 1, ...}. Least indices of prime(k) in a(n): i p(i) n a(n) --------------------- 1 2 1 4 2 3 2 6 3 5 5 15 4 7 18 63 5 11 59 308 6 13 49 234 7 17 68 374 8 19 84 475 9 23 292 2392 10 29 401 3625 11 31 518 4991 12 37 791 8547 ... MATHEMATICA Block[{nn = 2^10, r}, r = Array[If[# == 1, 0, Total[2^(PrimePi /@ FactorInteger[#][[All, 1]] - 1)]] &, nn]; Map[PrimePi@ FactorInteger[#][[-1, 1]] &, #] &@ Union@ Array[Block[{k = # + 1, s = r[[#]]}, While[UnsameQ[s, Set[s, BitOr[s, r[[k]] ] ] ], k++]; k] &, nn - Ceiling@ Sqrt@ nn] ] CROSSREFS Cf. A000720, A006530, A217287, A217438, A334468. Sequence in context: A249160 A346913 A269970 * A252230 A036043 A333486 Adjacent sequences: A333515 A333516 A333517 * A333519 A333520 A333521 KEYWORD nonn AUTHOR Michael De Vlieger, May 05 2020 STATUS approved

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Last modified March 23 03:46 EDT 2023. Contains 361434 sequences. (Running on oeis4.)