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

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..8.

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A087167 (a subsequence).

Cf. A059609.

Sequence in context: A038248 A046831 A003226 * A137081 A137079 A163658

Adjacent sequences: A088831 A088832 A088833 * A088835 A088836 A088837

Keyword

nonn,more

Author

Labos Elemer, Oct 29 2003

Extensions

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

Status

approved