A281818 - OEIS

%I #24 Oct 19 2019 04:12:14

%S 5,130,13,104,1,71,19

%N a(n) is the least number k such that sigma(n) + sigma(k) = sigma(abs(n-k)), or -1 if such a number does not exist.

%C a(8) > 10^14 unless a(8) = -1. (It's relatively easy to test because k needs to be a square or twice a square.) - _Charles R Greathouse IV_ , Feb 03 2017

%H Paolo P. Lava, <a href="/A281818/a281818.txt">First 250 terms, with -1 if it appears that k may not exist</a>

%e a(1) = 5 because 5 is the least number such that sigma(1) + sigma(5) = 1 + 6 = 7 = sigma(5-1).

%p with(numtheory): P:= proc(q) local k,n; for n from 1 to q do for k from 1 to q do

%p if sigma(n)+sigma(k)=sigma(abs(n-k)) then print(k); break; fi;

%p od; if k=q+1 then print(-1); fi; od; end: P(10^6);

%t Table[SelectFirst[Range[10^6], DivisorSigma[1, n] + DivisorSigma[1, #] == DivisorSigma[1, Abs[n - #]] &] /. k_ /; MissingQ@ k -> -1, {n, 58}] (* _Michael De Vlieger_, Feb 01 2017, Version 10.2 *)

%Y Cf. A000203.

%K sign,more

%O 1,1

%A _Paolo P. Lava_, Jan 31 2017