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A376141
The maximum exponent in the prime factorization of the numbers k such that k and k+1 have the same maximum exponent in their prime factorization.
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,17
LINKS
FORMULA
a(n) = A051903(A369020(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (d(2) + Sum_{k>=2} k * (d(k) + d(k+1) - 2 * d2(k)))/d0 = 1.14396758638154735362..., where d(k) = Product_{p prime} (1 - 2/p^k), d2(k) = Product_{p prime} (1 - 1/p^k - 1/p^(k+1)), and d0 = 0.36939178586283962461... is the asymptotic density of A369020.
MATHEMATICA
emax[n_] := Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; With[{t = Table[emax[n], {n, 1, 500}]}, t[[Position[Differences[t], 0] // Flatten]]]
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(e1, ", ")); e1 = e2); }
CROSSREFS
Sequence in context: A086011 A124760 A077619 * A030600 A079700 A357722
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 11 2024
STATUS
approved