A380233 Odd abundant numbers not divisible by 5 that are also doublets (cf. A020338).

153153, 171171, 189189, 207207, 243243, 261261, 279279, 297297, 351351, 459459, 513513, 567567, 621621, 729729, 783783, 837837, 891891, 999999, 1392313923, 1556115561, 1719917199, 1883718837, 2034920349, 2211322113, 2375123751, 2538925389, 2702727027, 3194131941, 4176941769, 4668346683

Offset

1,1

Comments

There are 26 odd abundant numbers not divisible by 5 less than 10^6. The surprising fact is that 18 of them are doublets.

Another interesting fact is that here there are no terms with 8 digits.

Links

Alexander Violette, Table of n, a(n) for n = 1..2773

Maple

doublet:= n -> n * (10^(1+ilog10(n))+1):
select(t -> numtheory:-sigma(t) > 2*t, [seq(seq(doublet(10*x+i), i=[1, 3, 7, 9]), x=1..10000)]); # Robert Israel, Jan 17 2025

Mathematica

Select[Table[FromDigits[Join[#, #] &@ IntegerDigits[n]], {n, Select[Range[50000], CoprimeQ[#, 10] &]}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Jan 17 2025 *)

Prog

(PARI) select(x->((x%5) && (sigma(x)>2*x)), vector(50000, n, eval(Str(2*n-1, 2*n-1)))) \\ Michel Marcus, Jan 17 2025

Crossrefs

Intersection of A064001 and A020338.

Cf. A005101, A005231, A047201.

Sequence in context: A233947 A172732 A172789 * A248594 A339528 A234553

Adjacent sequences: A380230 A380231 A380232 * A380234 A380235 A380236

Keyword

nonn,base

Author

Omar E. Pol, Jan 17 2025

Extensions

More terms from Michel Marcus, Jan 17 2025

Status

approved