cp's OEIS Frontend

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

%I A385451 #6 Jul 04 2025 19:48:59
%S A385451 5,11,14,7,10,71,13,101,48,129,18,17,46,37,22,27,62,35,28,55,66,3279,
%T A385451 92,49,42,155,32,1721,154,81,50,59,38,229,152,53,222,859,58,393,190,
%U A385451 45,52,73,68,97,104,60,128,63,72,87,436,401,136,673,142,429,272,163
%N A385451 Least integer k such that the sum of its anti-divisors is equal to k + n.
%e A385451 a(0) = 5: anti-divisors are 2, 3 and 2 + 3 - 5 = 0;
%e A385451 a(1) = 11: anti-divisors are 2, 3, 7 and 2 + 3 + 7 - 11 = 1;
%e A385451 a(2) = 14: anti-divisors are 3, 4, 9 and 3 + 4 + 9 - 14 = 2;
%e A385451 a(3) = 7: anti-divisors are 2, 3, 5 and 2 + 3 + 5 - 7 = 3.
%p A385451 with(numtheory): P:=proc(q,h) local a,b,j,k,n,v; v:=array(1..h);
%p A385451 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
%p A385451 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 A385451 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 A385451 P(3300,60);
%Y A385451 Cf. A066417, A385490.
%K A385451 nonn,easy
%O A385451 0,1
%A A385451 _Paolo P. Lava_, Jun 29 2025