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 A355661 Largest number of children of any vertex in the rooted tree with Matula-Goebel number n. 2
 0, 1, 1, 2, 1, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 4, 2, 3, 3, 3, 2, 2, 2, 4, 2, 2, 3, 3, 2, 3, 1, 5, 2, 2, 2, 4, 3, 3, 2, 4, 2, 3, 2, 3, 3, 2, 2, 5, 2, 3, 2, 3, 4, 4, 2, 4, 3, 2, 2, 4, 3, 2, 3, 6, 2, 3, 3, 3, 2, 3, 3, 5, 2, 3, 3, 3, 2, 3, 2, 5, 4, 2, 2, 4, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Record highs are at a(2^k) = k which is a root with k singleton children. A new root above a tree has a single child (the old root) so no change to the largest number of children, except when above a singleton, so that a(prime(n)) = a(n) for n >= 2. Terms a(n) <= 1 are paths down (all vertices 0 or 1 children), which are the primeth recurrence n = A007097. LINKS Kevin Ryde, Table of n, a(n) for n = 1..10000 Index entries for sequences related to Matula-Goebel numbers FORMULA a(n) = max(bigomega(n), {a(primepi(p)) | p prime factor of n}). a(n) = Max_{s in row n of A354322} bigomega(s). EXAMPLE For n=629, tree 629 is as follows and vertex 12 has 3 children which is the most of any vertex so that a(629) = 3. 629 root / \ 7 12 tree n=629 and its | /|\ subtree numbers 4 1 1 2 / \ | 1 1 1 MAPLE a:= proc(n) option remember; uses numtheory; max(bigomega(n), map(p-> a(pi(p)), factorset(n))[]) end: seq(a(n), n=1..100); # Alois P. Heinz, Jul 14 2022 MATHEMATICA nn = 105; a = 0; a = 1; Do[a[n] = Max@ Append[Map[a[PrimePi[#]] &, FactorInteger[n][[All, 1]]], PrimeOmega[n]], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Jul 14 2022 *) PROG (PARI) a(n) = my(f=factor(n)); vecmax(concat(vecsum(f[, 2]), [self()(primepi(p)) |p<-f[, 1]])); CROSSREFS Cf. A001222 (bigomega), A354322 (distinct subtrees). Cf. A007097 (indices of <=1). Cf. A355662 (minimum children). Sequence in context: A052304 A049874 A060501 * A109129 A304486 A188550 Adjacent sequences: A355658 A355659 A355660 * A355662 A355663 A355664 KEYWORD nonn AUTHOR Kevin Ryde, Jul 14 2022 STATUS approved

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Last modified October 1 20:32 EDT 2023. Contains 365828 sequences. (Running on oeis4.)