A380233 - OEIS

%I #55 Apr 03 2026 07:31:31

%S 153153,171171,189189,207207,243243,261261,279279,297297,351351,

%T 459459,513513,567567,621621,729729,783783,837837,891891,999999,

%U 1392313923,1556115561,1719917199,1883718837,2034920349,2211322113,2375123751,2538925389,2702727027,3194131941,4176941769,4668346683

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

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

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

%H Alexander Violette, <a href="/A380233/b380233.txt">Table of n, a(n) for n = 1..2773</a>

%p doublet:= n -> n * (10^(1+ilog10(n))+1):

%p 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

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

%o (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

%Y Intersection of A064001 and A020338.

%Y Cf. A005101, A005231, A047201.

%K nonn,base

%O 1,1

%A _Omar E. Pol_, Jan 17 2025

%E More terms from _Michel Marcus_, Jan 17 2025