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

Author

Amiram Eldar, Sep 17 2024

Keywords

• nonn
• easy

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

Crossrefs

Subsequence of A013929.

Subsequences: A067259, A325241, A376249.

Cf. A002117, A013661, A051903, A375933.

Programs

Mathematica

q[k_] := Module[{e = Union[FactorInteger[k][[;; , 2]]]}, Length[e] > 1 && e[[-2]] + 1 == e[[-1]]]; Select[Range[300], q]

PARI

is(k) = {my(e = Set(factor(k)[, 2])); #e > 1 && e[#e-1] + 1 == e[#e]; }