cp's OEIS Frontend

A385490 Least integer k such that the sum of its anti-divisors is equal to k - n.

%I A385490 #5 Jul 04 2025 19:49:47
%S A385490 5,1,2,261,34,29,194,7611,216,51,1164,1251,1044,239,236,69,226,749,64,
%T A385490 1079,156,79,114,219,2546,89,254,879,106,541,344,1619,96,531,454,991,
%U A385490 293606,10879,134,141,1006,491,146,509,1214,639,366,13649,35856,17081,726
%N A385490 Least integer k such that the sum of its anti-divisors is equal to k - n.
%e A385490 a(0) = 5: anti-divisors are 2, 3 and 5 - (2 + 3) = 0;
%e A385490 a(1) = 1: no anti-divisors and 1 - 0 = 1;
%e A385490 a(2) = 2: no anti-divisors and 2 - 0 = 2;
%e A385490 a(3) = 261: anti-divisors are 2, 6, 18, 58, 174 and 261 - (2 + 6 + 18 + 58 + 174) = 3.
%p A385490 with(numtheory): P:=proc(q,h) local a,b,j,k,n,v; v:=array(1..h);
%p A385490 for k from 1 to h do v[k]:=0; od; v[2]:=1; v[3]:=2;
%p A385490 for n from 3 to q do k:=0; j:=n; while j mod 2<>1 do
%p A385490 k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A385490 if n>=a then b:=n-a+1; if b<=h then if v[b]=0 then v[b]:=n; fi; fi; fi; od; op(v); end:
%p A385490 P(293606,51);
%Y A385490 Cf. A066417, A385451.
%K A385490 nonn,easy
%O A385490 0,1
%A A385490 _Paolo P. Lava_, Jun 30 2025