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A369021 Numbers k such that k, k+1 and k+2 have the same maximal exponent in their prime factorization. 3
5, 13, 21, 29, 33, 37, 41, 57, 65, 69, 77, 85, 93, 98, 101, 105, 109, 113, 129, 137, 141, 157, 165, 177, 181, 185, 193, 201, 209, 213, 217, 221, 229, 237, 253, 257, 265, 281, 285, 301, 309, 317, 321, 329, 345, 353, 357, 365, 381, 389, 393, 397, 401, 409, 417, 429 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that A051903(k) = A051903(k+1) = A051903(k+2).
The asymptotic density of this sequence is d(2,3) + Sum_{k>=2} (d(k+1,3) - d(k,3) + 3*d2(k,2,1) - 3*d2(k,1,2)) = 0.13122214221443994377..., where d(k,m) = Product_{p prime} (1 - m/p^k) and d2(k,m1,m2) = Product_{p prime} (1 - m1/p^k - m2/p^(k+1)).
LINKS
MATHEMATICA
emax[n_] := emax[n] = Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; Select[Range[200], emax[#] == emax[# + 1] == emax[#+2] &]
PROG
(PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2]));
lista(kmax) = {my(e1 = 0, e2 = 0, e3); for(k = 3, kmax, e3 = emax(k); if(e1 == e2 && e2 == e3, print1(k-2, ", ")); e1 = e2; e2 = e3); }
CROSSREFS
Subsequence of A369020.
Subsequences: A007675, A071319.
Sequence in context: A197120 A319449 A030374 * A007675 A043441 A251537
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 12 2024
STATUS
approved

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)