|
|
A068414
|
|
Numbers k such that sigma(k) = 3k - 2*phi(k).
|
|
4
|
|
|
1, 12, 56, 260, 992, 1976, 2156, 2754, 16256, 25232, 41072, 133984, 145888, 1100864, 1270208, 1439552, 2237888, 4729664, 67100672, 75398912, 171627376, 277060144, 473089984, 538178048, 558585344, 629225984, 1192258048, 1863840112, 2181070592, 4534854656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
If 2^p-1 is prime (a Mersenne prime) and n = 2^p*(2^p-1) then n is in the sequence because 3*n-2*phi(n) = 3*2^p*(2^p-1)-2^p*(2^p-2) = 2^p*(2^(p+1)-1) = sigma(2^p-1)*sigma(2^p) = sigma(2^p*(2^p-1)) = sigma(n). - Farideh Firoozbakht, Dec 31 2005
|
|
LINKS
|
|
|
MATHEMATICA
|
Select[Range[10^6], DivisorSigma[1, #] == 3*# - 2*EulerPhi[#] &] (* Amiram Eldar, May 14 2022 *)
|
|
PROG
|
(PARI) for(n=1, 500000, if(sigma(n)==3*n-2*eulerphi(n), print1(n, ", ")))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|