[seqfan] Empirical relation for A180169: Sigma(A180162(n)), where A180162(n) is the smallest N such that sigma(N) is an nth power, or 0 if no such N can be found

[Georgi Guninski]

A180169: Sigma(A180162(n)), where A180162(n) is the smallest N such that sigma(N) is an nth power, or 0 if no such N can be found

appears to satisfy for the first 465 terms (the B-File):

a(n+2) = -(4*(n - 12)*a(n - 1) - 3*(n - 10)*a(n + 1))/(n - 9)

this is the only potential relation involving sigma that i found.

is there a fast ways to compute more terms to check?