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 A340109 Coreful 3-abundant numbers: numbers k such that csigma(k) > 3*k, where csigma(k) is the sum of the coreful divisors of k (A057723). 2
 5400, 7200, 10800, 14400, 16200, 18000, 21168, 21600, 27000, 28800, 32400, 36000, 37800, 42336, 43200, 48600, 50400, 54000, 56448, 57600, 59400, 63504, 64800, 70200, 72000, 75600, 79200, 81000, 84672, 86400, 88200, 90000, 91800, 93600, 97200, 98784, 100800, 102600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 A068403 as A308053 is analogous to A005101. Apparently, the least odd term in this sequence is 3^4 * 5^3 * 7^3 * 11^2 * 13^2 * 17^2 * 19^2 * 23^2 * 29^2 = 3296233276111741840875. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 5400 is a term since csigma(5400) = 16380 > 3 * 5400. MATHEMATICA f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^5], s[#] > 3*# &] CROSSREFS Subsequence of A308053. Cf. A007947, A057723. Similar sequences: A068403, A285615, A293187, A300664, A307112, A328135. Sequence in context: A335936 A335939 A328562 * A190106 A252572 A035902 Adjacent sequences:  A340106 A340107 A340108 * A340110 A340111 A340112 KEYWORD nonn AUTHOR Amiram Eldar, Dec 28 2020 STATUS approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)