OFFSET
2,2
COMMENTS
The offset is 2, because for all numbers m, phi(m)+sigma(m) >= 2*m, so there is no number a(1) such that phi(a(1))+sigma(a(1))=1*a(1). - Farideh Firoozbakht, Jan 22 2008
a(5) >= 2*10^9. - Farideh Firoozbakht, Jan 22 2008
10^13 < a(5) <= 336280120525440. Charles R Greathouse IV showed that 6 divides a(5). 336280120525440 and 60493590969525342720 are the only m values I found such that phi(m) + sigma(m) = 5*m. - Donovan Johnson, Sep 11 2012
LINKS
Richard K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.
PROG
(PARI) a(n) = my(m = 1); while(sigma(m)+eulerphi(m) != n*m, m++); m; \\ Michel Marcus, Oct 04 2017
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
Name, offset and data corrected by Farideh Firoozbakht, Jan 22 2008
a(5) confirmed by Martin Ehrenstein, Jan 15 2024
STATUS
approved