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%I #25 Aug 05 2023 04:12:41
%S 945,4095,6435,7425,8415,8925,9555,26145,28035,30555,31815,32445,
%T 43065,46035,78975,80535,81081,103455,129195,182655,191565,261261,
%U 279279,351351,354585,355725,371925,403095,411255,430815,437745,442365,458055
%N Odd admirable numbers: such that sigma(n) = 2n + 2d for some d | n.
%C Equivalently: Odd n such that sigma(n)/2 - n is a positive divisor of n. (Negative and/or half-integer d = sigma(n)/2 - n, of which n could be a multiple, are excluded. Negative d correspond to deficient n, half-integer d to square n: the first example of an abundant n being a multiple of a half-integer d is n = 13167^2 = 173369889.) - _M. F. Hasler_, Jan 26 2020
%H Amiram Eldar, <a href="/A109729/b109729.txt">Table of n, a(n) for n = 1..746</a> (terms below 3*10^12)
%o (PARI) select( {is_A109729(n,s=sigma(n))=s>2*n&&n%(s/2-n)==0&&n%2&&!(s%2)}, [2*k-1|k<-[1..5e5\2]]) \\ _M. F. Hasler_, Jan 26 2020
%Y Cf. A111592 (admirable numbers).
%Y Cf. A000203 (sigma: sum of divisors).
%K nonn
%O 1,1
%A _Jason Earls_, Aug 09 2005
%E Offset corrected by _Amiram Eldar_, Jun 22 2019
%E Name edited by _M. F. Hasler_, Jan 26 2020
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