A369020 Numbers k such that k and k+1 have the same maximal exponent in their prime factorization.

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

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