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A109729 Odd admirable numbers: such that sigma(n) = 2n + 2d for some d | n. 7
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..746 (terms below 3*10^12)
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
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 March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)