A380232 Odd abundant numbers that are also doublets (cf. A020338).
105105, 135135, 153153, 165165, 171171, 189189, 195195, 207207, 225225, 243243, 255255, 261261, 279279, 285285, 297297, 315315, 345345, 351351, 375375, 405405, 435435, 459459, 465465, 495495, 513513, 525525, 555555, 567567, 585585, 615615, 621621, 645645, 675675, 705705, 729729, 735735, 765765, 783783, 795795, 825825, 837837
Offset: 1
Examples
a(1) = 105105 is an odd abundant number (cf. A005231) because it is and odd number and the sum of its divisors is equal to 229824 which exceeds 2*105105 = 210210. Also 105105 is a doublet (cf. A020338) because it is 105||105, that is the concatenation of 105 and 105, so 105105 is in the sequence.
Programs
-
Mathematica
Select[Table[FromDigits[Join[#, #] &@ IntegerDigits[n]], {n, 1, 850, 2}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Jan 18 2025 *) -
PARI
select(x->(sigma(x)>2*x), vector(1000, n, eval(Str(2*n-1, 2*n-1)))) \\ Michel Marcus, Jan 18 2025