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%I #11 Oct 20 2023 06:46:31
%S 1157625,10418625,12733875,15049125,19679625,21994875,26625375,
%T 28940625,33571125,35886375,40429125,42832125,47462625,49777875,
%U 54408375,56723625,61354125,66733875,68299875,70615125,77560875,82191375,84506625,91452375,93767625,96082875
%N Coreful abundant numbers (A308053) with an odd sum of coreful divisors.
%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 All the terms are odd numbers since the sum of coreful divisors (A057723) of an even number is even.
%C All the terms are exponentially odd numbers (A268335) since the sum of coreful divisors function is multiplicative and A057723(p^e) = p + p^2 + ... + p^e is even for a prime p and an even exponent e.
%C None of the terms are coreful Zumkeller numbers (A339979).
%H Amiram Eldar, <a href="/A339982/b339982.txt">Table of n, a(n) for n = 1..1000</a>
%e 1157625 is a term since A057723(1157625) = 2411955 > 2*1157625 and it is odd.
%t f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[1, 2*10^7, 2], (sum = s[#]) > 2*# && OddQ[sum] &]
%Y Intersection of A268335 and A339936.
%Y Subsequence of A308053.
%Y Cf. A007947, A057723, A339979.
%K nonn
%O 1,1
%A _Amiram Eldar_, Dec 25 2020
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