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A067702
Numbers k such that sigma(k) == 0 (mod k+2).
15
12, 70, 88, 180, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470
OFFSET
1,1
COMMENTS
a(12) > 10^8. - Michel Marcus, Nov 22 2013
If 2^i-5 is prime for i > 2 then let x = (2^i-5)*2^(i-1). Then sigma(x)=2*(x+2), so x is in the sequence. There are other terms that are not of this form. - Jud McCranie, Jan 12 2019
EXAMPLE
sigma(180) = 546 = 3(180+2), so 180 is in the sequence.
MATHEMATICA
Select[Range[84*10^5], Divisible[DivisorSigma[1, #], #+2]&] (* Harvey P. Dale, May 11 2018 *)
PROG
(PARI) isok(n) = sigma(n) % (n+2) == 0; \\ Michel Marcus, Nov 22 2013
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Benoit Cloitre, Feb 05 2002
EXTENSIONS
a(9)-a(11) from Michel Marcus, Nov 22 2013
a(12)-a(13) from Jud McCranie, Jan 12 2019
a(14) from Jud McCranie, Jan 13 2019
a(15) from Jud McCranie, Dec 02 2019
STATUS
approved