A376251 Numbers that have a second-largest exponent in their prime factorization and it is smaller by 1 than the largest exponent.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Cf. A002117, A013661, A051903, A375933.

Sequence in context: A187039 A360554 A325241 * A376249 A072357 A340780

Adjacent sequences: A376248 A376249 A376250 * A376252 A376253 A376254

Keyword

nonn,easy

Author

Amiram Eldar, Sep 17 2024

Status

approved