A387154 The least number k that is not n-free whose sum of n-free divisors is larger than 2*k.

401120980260, 360360, 55440, 110880, 100800, 120960, 241920, 483840, 967680, 1935360, 3870720, 7741440, 15482880, 30965760, 61931520, 123863040, 247726080, 495452160, 990904320, 1981808640, 3963617280, 7927234560, 15854469120, 31708938240, 63417876480, 126835752960

Offset

2,1

Comments

n-free numbers are numbers that are not divisible by an n-th power larger than 1. E.g., A005117, A004709, and A046100 for n = 2, 3, and 4, respectively.

The sum of n-free divisors of a number is the sum of its divisors that are n-free numbers. E.g., A048250, A073185, and A385006 for n = 2, 3, and 4, respectively.

All the terms are in A025487.

Links

Amiram Eldar, Table of n, a(n) for n = 2..1000

Formula

a(n) = 945 * 2^n for n >= 7.

Example

For n = 2, the numbers k such that A048250(k) > 2*k include all the squarefree abundant numbers (A087248). The least nonsquarefree number (A013929) k such that A048250(k) > 2*k is 401120980260 = 2^2*3*5*7*11*13*17*19*23*29*31.
For n = 3, the numbers k such that A073185(k) > 2*k include all the cubefree abundant numbers (A357695). The least noncubefree number (A046099) k such that A073185(k) > 2*k is A357700(1) = 360360 = 2^3*3^2*5*7*11*13.

Mathematica

a[n_] := If[n < 7, {401120980260, 360360, 55440, 110880, 100800}[[n-1]], 945 * 2^n]; Array[a, 26, 2]

Prog

(PARI) a(n) = if(n < 7, [401120980260, 360360, 55440, 110880, 100800][n-1], 945 * 2^n);

Crossrefs

Cf. A004709, A005117, A013929, A025487, A046099, A046100, A048250, A087248, A073185, A357695, A357700, A385006, A387155.

Sequence in context: A269417 A281963 A379490 * A357687 A363799 A082411

Adjacent sequences: A387151 A387152 A387153 * A387155 A387156 A387157

Keyword

nonn

Author

Amiram Eldar, Aug 19 2025

Status

approved