A281818 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.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..7.

Paolo P. Lava, First 250 terms, with -1 if it appears that k may not exist

Example

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

Maple

with(numtheory): P:= proc(q) local k, n; for n from 1 to q do for k from 1 to q do
if sigma(n)+sigma(k)=sigma(abs(n-k)) then print(k); break; fi;
od; if k=q+1 then print(-1); fi; od; end: P(10^6);

Mathematica

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 *)

Crossrefs

Cf. A000203.

Sequence in context: A012187 A012083 A012226 * A332317 A069078 A003732

Adjacent sequences: A281815 A281816 A281817 * A281819 A281820 A281821

Keyword

sign,more

Author

Paolo P. Lava, Jan 31 2017

Status

approved