A015704 a(n) is the smallest number m such that phi(m) + sigma(m) = n*m.

1, 312, 23760, 336280120525440

Offset: 2

Author

Robert G. Wilson v

Keywords

• nonn
• hard
• more

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.

Crossrefs

Cf. A011251, A011254.

Programs

PARI

a(n) = my(m = 1); while(sigma(m)+eulerphi(m) != n*m, m++); m; \\ Michel Marcus, Oct 04 2017

Extensions

Name, offset and data corrected by Farideh Firoozbakht, Jan 22 2008

a(5) confirmed by Martin Ehrenstein, Jan 15 2024