5 consecutive integers with sigma(A) coprime to A

[Jack Brennen]

A very sparse sequence defined as:

Positive integers N such that for every A in [N,N+1,N+2,N+3,N+4]
we have sigma(A) coprime with A.

Terms are:
1
575
202605639573839041
478502736827135487987972323577847681

Any other terms exceed 10^128.


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.