A369021 Numbers k such that k, k+1 and k+2 have the same maximal exponent in their prime factorization.

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

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

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] == 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

Cf. A051903, A369022.

Subsequence of A369020.

Subsequences: A007675, A071319.

Sequence in context: A197120 A319449 A030374 * A007675 A043441 A251537

Adjacent sequences: A369018 A369019 A369020 * A369022 A369023 A369024

Keyword

nonn,easy

Author

Amiram Eldar, Jan 12 2024

Status

approved