

A109729


Odd admirable numbers: such that sigma(n) = 2n + 2d for some d  n.


5



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 halfinteger d = sigma(n)/2  n, of which n could be a multiple, are excluded. Negative d correspond to deficient n, halfinteger d to square n: the first example of an abundant n being a multiple of a halfinteger 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/2n)==0&&n%2&&!(s%2)}, [2*k1k<[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



