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 A109729 Odd admirable numbers: such that sigma(n) = 2n + 2d for some d | n. 3
 945, 4095, 6435, 7425, 8415, 8925, 9555, 26145, 28035, 30555, 31815, 32445, 43065, 46035, 78975, 80535, 81081, 103455, 129195, 182655, 191565, 261261, 279279, 351351, 354585, 355725, 371925, 403095, 411255, 430815, 437745, 442365, 458055 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Amiram Eldar, Table of n, a(n) for n = 1..100 PROG (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 CROSSREFS Cf. A111592 (admirable numbers). Cf. A000203 (sigma: sum of divisors). Sequence in context: A252184 A188263 A188342 * A294025 A275449 A293186 Adjacent sequences:  A109726 A109727 A109728 * A109730 A109731 A109732 KEYWORD nonn AUTHOR Jason Earls, Aug 09 2005 EXTENSIONS Offset corrected by Amiram Eldar, Jun 22 2019 Name edited by M. F. Hasler, Jan 26 2020 STATUS approved

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Last modified May 25 02:01 EDT 2020. Contains 334581 sequences. (Running on oeis4.)