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

1,1

Links

Table of n, a(n) for n=1..41.

Example

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.

Mathematica

Select[Table[FromDigits[Join[#, #] &@ IntegerDigits[n]], {n, 1, 850, 2}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Jan 18 2025 *)

Prog

(PARI) select(x->(sigma(x)>2*x), vector(1000, n, eval(Str(2*n-1, 2*n-1)))) \\ Michel Marcus, Jan 18 2025

Crossrefs

Intersection of A005231 and A020338.

A subsequence is A380233.

Cf. A005101, A064001.

Sequence in context: A202934 A203822 A013889 * A353553 A025308 A025290

Adjacent sequences: A380228 A380229 A380230 * A380233 A380234 A380235

Keyword

nonn,base

Author

Omar E. Pol, Jan 17 2025

Status

approved