A370409 - OEIS

A370409

Numbers k = m * s, where s is composite and squarefree, rad(m) divides s, and 1 < m <= s, where rad() = A007947().

12, 18, 20, 24, 28, 36, 40, 44, 45, 50, 52, 56, 60, 63, 68, 75, 76, 80, 84, 88, 90, 92, 98, 99, 100, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 196, 198, 204, 207, 208

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OFFSET

1,1

COMMENTS

A177492 is a proper subset.

Proper subset of A126706.

This sequence is { k : A001221(k) > 1, A003557(k) <= A007947(k) } = intersection of A126706 and A390538. - Michael De Vlieger, Nov 09 2025

A126706 is the union of this sequence and A389528. - Michael De Vlieger, Nov 13 2025

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

Let T(j,k) = row j of A162306 and let s = A120944(n), n > 1.

This sequence contains finite sequences R(s) = s * T(s, 2..A010846(s)). The cardinality of R(s) is A010846(s)-1.

For s = 6, this sequence contains {12, 18, 24, 36},

i.e., A033845(2..A010846(6)).

For s = 10, this sequence contains {20, 40, 50, 80, 100},

i.e., A033846(2..A010846(10)).

For s = 14, this sequence contains {28, 56, 98, 112, 196},

i.e., A033847(2..A010846(14)).

For s = 15, this sequence contains {45, 75, 135, 225},

i.e., A033849(2..A010846(15)), etc.

MATHEMATICA

Select[Range[210], And[#2 > 1, #3 < #1 <= #3^2] & @@ {#1, Length[#2], Times @@ #2} & @@ {#, FactorInteger[#][[;; , 1]]} &] (* Michael De Vlieger, Nov 09 2025 *)

CROSSREFS

Cf. A005117, A007947, A120944, A126706, A162306, A177492, A370266, A389528, A390538.

Sequence in context: A126706 A123711 A200511 * A363101 A369516 A317711

Adjacent sequences: A370406 A370407 A370408 * A370410 A370411 A370412

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Feb 22 2024

STATUS

approved