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

Author

Omar E. Pol, Jan 17 2025

Keywords

• nonn
• base

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.

Crossrefs

Intersection of A064001 and A020338.

Cf. A005101, A005231, A047201.

Programs

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 *)

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

Extensions

More terms from Michel Marcus, Jan 17 2025