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A376251
Numbers that have a second-largest exponent in their prime factorization and it is smaller by 1 than the largest exponent.
1
12, 18, 20, 28, 44, 45, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 98, 99, 108, 116, 117, 124, 126, 132, 140, 147, 148, 150, 153, 156, 164, 171, 172, 175, 180, 188, 198, 200, 204, 207, 212, 220, 228, 234, 236, 242, 244, 245, 252, 260, 261, 268, 275, 276, 279
OFFSET
1,1
COMMENTS
First differs from its subsequence A325241 at n = 74: a(74) = 360 = 2^3 * 3^2 * 5 is not a term of A325241.
Numbers k such that 0 < A375933(k) = A051903(k) - 1.
The asymptotic density of this sequence is Sum_{k>=2} d(k) = 0.24179287499021146826..., where d(2) = 1/zeta(3) - 1/zeta(2), and d(k) = 1/zeta(k+1) - 1/zeta(k) + 1/zeta(k-1) - Product_{p prime} (1 - 1/p^(k-1) + 1/p^k - 1/p^(k+1)) for k >= 3.
LINKS
MATHEMATICA
q[k_] := Module[{e = Union[FactorInteger[k][[;; , 2]]]}, Length[e] > 1 && e[[-2]] + 1 == e[[-1]]]; Select[Range[300], q]
PROG
(PARI) is(k) = {my(e = Set(factor(k)[, 2])); #e > 1 && e[#e-1] + 1 == e[#e]; }
CROSSREFS
Subsequence of A013929.
Subsequences: A067259, A325241, A376249.
Sequence in context: A187039 A360554 A325241 * A376249 A072357 A340780
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 17 2024
STATUS
approved