A088834 Numbers k such that sigma(k) == 6 (mod k).

1, 5, 6, 25, 180, 8925, 32445, 442365

Offset: 1

Author

Labos Elemer, Oct 29 2003

Keywords

• nonn
• more

Comments

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

No more terms to 10^10. - Charles R Greathouse IV, Dec 05 2013

a(9) > 10^13. - Giovanni Resta, Apr 02 2014

a(9) > 1.5*10^14. - Jud McCranie, Jun 02 2019

No more terms < 2.7*10^15. - Jud McCranie, Jul 27 2025

Examples

			Sigma(25) = 31 = 1*25 + 6, so 31 mod 25 = 6.
		

Links

• Farideh Firoozbakht and M. F. Hasler, Variations on Euclid's formula for perfect numbers, Journal of Integer Sequences 13 (2010), 18 pp. Article ID 10.3.1.

Crossrefs

Cf. A054024, A045768, A045769, A045770, A077374, A076496, A088012.

Cf. A087167 (a subsequence).

Cf. A059609.

Programs

Mathematica

Select[Range[1000000], Mod[DivisorSigma[1, #] - 6, #] == 0 &] (* T. D. Noe, Dec 03 2013 *)

PARI

isok(n) = Mod(sigma(n), n) == 6; \\ Michel Marcus, Jan 03 2023

Extensions

Terms corrected by Charles R Greathouse IV and Farideh Firoozbakht, Dec 03 2013