A375934 Numbers whose prime factorization has a second-largest exponent that equals 1.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 204

Offset

1,1

Comments

First differs from A332785 at n = 112: A332785(112) = 360 = 2^3 * 3^2 * 5 is not a term of this sequence.

First differs from A317616 at n = 38: A317616(38) = 144 = 2*4 * 3^2 is not a term of this sequence.

Numbers k such that A375933(k) = 1.

Numbers of the form s1 * s2^e, where s1 and s2 are coprime squarefree numbers that are both larger than 1, and e >= 2.

The asymptotic density of this sequence is Sum_{e>=2} d(e) = 0.36113984820338109927..., where d(e) = Product_{p prime} (1 - 1/p^2 + 1/p^e - 1/p^(e+1)) - Product_{p prime} (1 - 1/p^(e+1)) is the asymptotic density of terms k with A051903(k) = e >= 2.

Links

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

Formula

A051904(a(n)) = 1.

A051903(a(n)) >= 2.

A001221(a(n)) = 2.

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[0, Max[Select[e, # < Max[e] &]]] == 1]; Select[Range[300], q]

Prog

(PARI) is(n) = if(n == 1, 0, my(e = factor(n)[, 2]); e = select(x -> x < vecmax(e), e); if(#e == 0, 0, vecmax(e) == 1));

Crossrefs

Equals A375142 \ A072777.

Subsequence of A013929.

Subsequences: A054753, A065036, A072357, A095990, A096156, A178739, A178740, A179664, A179668, A179692, A189987, A360793, A375076.

Cf. A001221, A005117, A051903, A051904, A072777, A317616, A332785, A375142, A375933.

Sequence in context: A242416 A360248 A317616 * A332785 A367589 A177425

Adjacent sequences: A375931 A375932 A375933 * A375935 A375936 A375937

Keyword

nonn,easy

Author

Amiram Eldar, Sep 03 2024

Status

approved