A015704 - OEIS

%I #36 Jan 16 2024 01:57:54

%S 1,312,23760,336280120525440

%N a(n) is the smallest number m such that phi(m) + sigma(m) = n*m.

%C 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

%C a(5) >= 2*10^9. - _Farideh Firoozbakht_, Jan 22 2008

%C 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

%H Richard K. Guy, <a href="http://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360.

%o (PARI) a(n) = my(m = 1); while(sigma(m)+eulerphi(m) != n*m, m++); m; \\ _Michel Marcus_, Oct 04 2017

%Y Cf. A011251, A011254.

%K nonn,hard,more

%O 2,2

%A _Robert G. Wilson v_

%E Name, offset and data corrected by _Farideh Firoozbakht_, Jan 22 2008

%E a(5) confirmed by _Martin Ehrenstein_, Jan 15 2024