A136111 Positive integers n such that for every k in [n,n+1,n+2,n+3,n+4] we have sigma(k) coprime to k.

1, 575, 202605639573839041, 478502736827135487987972323577847681

Offset: 1

Author

Jack Brennen, Mar 17 2008

Keywords

• nonn

Comments

Note that it is impossible to have three consecutive positive even integers which have odd sigma() values.

In order to have an odd sigma() value, the integer must be a square or twice a square; it's not too hard to see that three consecutive positive even integers can't each be a square or twice a square.

So any solution must have n odd and among n+1 and n+3, one of them must be a square and the other must be twice a square.

Any other terms exceed 10^128.