cp's OEIS Frontend

A375389 a(n) is the smallest abundant number k such that n - k is abundant, or -1 if there is no such k.

%I A375389 #15 Aug 17 2024 22:28:25
%S A375389 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
%T A375389 12,-1,-1,-1,-1,-1,12,-1,12,-1,-1,-1,12,-1,18,-1,20,-1,12,-1,20,-1,-1,
%U A375389 -1,12,-1,20,-1,12,-1,12,-1,20,-1,18,-1,12,-1,20,-1,24,-1,12,-1,12,-1,30,-1,12,-1,18
%N A375389 a(n) is the smallest abundant number k such that n - k is abundant, or -1 if there is no such k.
%C A375389 a(n) >= 12 for n >= 20162.
%C A375389 a(n) = 12 if n >= 24 and n == 0 (mod 6).
%C A375389 12 <= a(n) <= 20 if n >= 26 and n == 2 (mod 6).
%C A375389 12 <= a(n) <= 40 if n >= 52 and n == 4 (mod 6).
%C A375389 If a(n) > 0 then 0 < a(k n - (k-1) a(n)) <= a(n) for all positive integers k.
%H A375389 Robert Israel, <a href="/A375389/b375389.txt">Table of n, a(n) for n = 1..21000</a>
%e A375389 a(30) = 12 because 30 = 12 + 18 where 12 and 18 are abundant numbers.
%p A375389 Ab:= select(t -> numtheory:-sigma(t) > 2*t, [$1..10^4]):
%p A375389 f:= proc(n) local i,x;
%p A375389   for i from 1 do
%p A375389     x:= Ab[i];
%p A375389     if 2*x > n then return -1 fi;
%p A375389     if ListTools:-BinarySearch(Ab, n-x) <> 0 then return x fi
%p A375389   od;
%p A375389 end proc:
%p A375389 map(f, [$1..100]);
%Y A375389 Cf. A005101, A048242.
%K A375389 sign,look
%O A375389 1,24
%A A375389 _Robert Israel_, Aug 13 2024