%I #42 Jan 04 2023 10:32:29
%S 1,5,6,25,180,8925,32445,442365
%N Numbers k such that sigma(k) == 6 (mod k).
%C For each integer j in A059609, 2^(j-1)*(2^j - 7) is in the sequence. E.g., for j = A059609(1) = 39 we get 151115727449904501489664. - _M. F. Hasler_ and _Farideh Firoozbakht_, Dec 03 2013
%C No more terms to 10^10. - _Charles R Greathouse IV_, Dec 05 2013
%C a(9) > 10^13. - _Giovanni Resta_, Apr 02 2014
%C a(9) > 1.5*10^14. - _Jud McCranie_, Jun 02 2019
%H Farideh Firoozbakht and M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for perfect numbers</a>, Journal of Integer Sequences 13 (2010), 18 pp. Article ID 10.3.1.
%e Sigma(25) = 31 = 1*25 + 6, so 31 mod 25 = 6.
%t Select[Range[1000000], Mod[DivisorSigma[1, #] - 6, #] == 0 &] (* _T. D. Noe_, Dec 03 2013 *)
%o (PARI) isok(n) = Mod(sigma(n), n) == 6; \\ _Michel Marcus_, Jan 03 2023
%Y Cf. A054024, A045768, A045769, A045770, A077374, A076496, A088012.
%Y Cf. A087167 (a subsequence).
%Y Cf. A059609.
%K nonn,more
%O 1,2
%A _Labos Elemer_, Oct 29 2003
%E Terms corrected by _Charles R Greathouse IV_ and _Farideh Firoozbakht_, Dec 03 2013