A340110 Coreful 4-abundant numbers: numbers k such that csigma(k) > 4*k, where csigma(k) is the sum of the coreful divisors of k (A057723).

10584000, 12700800, 15876000, 19051200, 21168000, 22226400, 25401600, 29635200, 31752000, 37044000, 38102400, 42336000, 44452800, 47628000, 50803200, 52920000, 55566000, 57153600, 59270400, 63504000, 64033200, 66679200, 74088000, 76204800, 79380000, 84672000

Offset: 1

Author

Amiram Eldar, Dec 28 2020

Keywords

• nonn

Comments

A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).

Analogous to A068404 as A308053 is analogous to A005101.

Examples

			10584000 is a term since csigma(10584000) = 42653520 > 4 * 10584000.
		

Links

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

Crossrefs

Subsequence of A308053 and A340109.

Cf. A007947, A057723.

Similar sequences: A068404, A307114.

Programs

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^8], s[#] > 4*# &]