A385451 Least integer k such that the sum of its anti-divisors is equal to k + n.

5, 11, 14, 7, 10, 71, 13, 101, 48, 129, 18, 17, 46, 37, 22, 27, 62, 35, 28, 55, 66, 3279, 92, 49, 42, 155, 32, 1721, 154, 81, 50, 59, 38, 229, 152, 53, 222, 859, 58, 393, 190, 45, 52, 73, 68, 97, 104, 60, 128, 63, 72, 87, 436, 401, 136, 673, 142, 429, 272, 163

Offset: 0

Author

Paolo P. Lava, Jun 29 2025

Keywords

• nonn
• easy

Examples

			a(0) = 5: anti-divisors are 2, 3 and 2 + 3 - 5 = 0;
a(1) = 11: anti-divisors are 2, 3, 7 and 2 + 3 + 7 - 11 = 1;
a(2) = 14: anti-divisors are 3, 4, 9 and 3 + 4 + 9 - 14 = 2;
a(3) = 7: anti-divisors are 2, 3, 5 and 2 + 3 + 5 - 7 = 3.
		

Crossrefs

Cf. A066417, A385490.

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; for n from 1 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 a>=n then b:=a-n+1; if b<=h then if v[b]=0 then v[b]:=n; fi; fi; fi; od; op(v); end:
P(3300,60);