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 A369020 Numbers k such that k and k+1 have the same maximal exponent in their prime factorization. 3
 2, 5, 6, 10, 13, 14, 21, 22, 29, 30, 33, 34, 37, 38, 41, 42, 44, 46, 49, 57, 58, 61, 65, 66, 69, 70, 73, 75, 77, 78, 80, 82, 85, 86, 93, 94, 98, 99, 101, 102, 105, 106, 109, 110, 113, 114, 116, 118, 122, 129, 130, 133, 135, 137, 138, 141, 142, 145, 147, 154, 157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A358817 by having the terms 99, 165, 166, ..., which are not in A358817, and not having the terms 1, 440, 1331, 1575, ..., which are in A358817. Numbers k such that A051903(k) = A051903(k+1). If k is a term then k*(k+1) is a term of A362605. The asymptotic density of this sequence is d(2) + Sum_{k>=2} (d(k) + d(k+1) - 2 * d2(k)) = 0.36939178586283962461..., where d(k) = Product_{p prime} (1 - 2/p^k) and d2(k) = Product_{p prime} (1 - 1/p^k - 1/p^(k-1)). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MATHEMATICA emax[n_] := emax[n] = Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; Select[Range[200], emax[#] == emax[# + 1] &] PROG (PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2])); lista(kmax) = {my(e1 = 0, e2); for(k = 2, kmax, e2 = emax(k); if(e1 == e2, print1(k-1, ", ")); e1 = e2); } CROSSREFS Cf. A051903, A358817, A362605, A369022. Subsequences: A007674, A071318, A369021. Sequence in context: A047440 A255055 A344314 * A358817 A369166 A369211 Adjacent sequences: A369017 A369018 A369019 * A369021 A369022 A369023 KEYWORD nonn,easy AUTHOR Amiram Eldar, Jan 12 2024 STATUS approved

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Last modified August 9 10:37 EDT 2024. Contains 375040 sequences. (Running on oeis4.)