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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).
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%I #8 Dec 29 2020 02:53:44

%S 10584000,12700800,15876000,19051200,21168000,22226400,25401600,

%T 29635200,31752000,37044000,38102400,42336000,44452800,47628000,

%U 50803200,52920000,55566000,57153600,59270400,63504000,64033200,66679200,74088000,76204800,79380000,84672000

%N 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).

%C 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).

%C Analogous to A068404 as A308053 is analogous to A005101.

%H Amiram Eldar, <a href="/A340110/b340110.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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*# &]

%Y Subsequence of A308053 and A340109.

%Y Cf. A007947, A057723.

%Y Similar sequences: A068404, A307114.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 28 2020