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

5, 1, 2, 261, 34, 29, 194, 7611, 216, 51, 1164, 1251, 1044, 239, 236, 69, 226, 749, 64, 1079, 156, 79, 114, 219, 2546, 89, 254, 879, 106, 541, 344, 1619, 96, 531, 454, 991, 293606, 10879, 134, 141, 1006, 491, 146, 509, 1214, 639, 366, 13649, 35856, 17081, 726

Offset: 0

Author

Paolo P. Lava, Jun 30 2025

Keywords

• nonn
• easy

Examples

			a(0) = 5: anti-divisors are 2, 3 and 5 - (2 + 3) = 0;
a(1) = 1: no anti-divisors and 1 - 0 = 1;
a(2) = 2: no anti-divisors and 2 - 0 = 2;
a(3) = 261: anti-divisors are 2, 6, 18, 58, 174 and 261 - (2 + 6 + 18 + 58 + 174) = 3.
		

Crossrefs

Cf. A066417, A385451.

Programs

Maple

with(numtheory): P:=proc(q,h) local a,b,j,k,n,v; v:=array(1..h);
for k from 1 to h do v[k]:=0; od; v[2]:=1; v[3]:=2;
for n from 3 to q do k:=0; j:=n; while j mod 2<>1 do
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;
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(293606,51);