A084820 Numbers n such that n, sigma(n) and phi(n) form an integer triangle, where sigma=A000203 is the divisor sum and phi=A000010 the totient.

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 137

Offset: 1

Author

Reinhard Zumkeller, Jun 04 2003

Keywords

• nonn

Comments

a(n)<=A000203(a(n))+A000010(a(n)), A000203(a(n))<=a(n)+A000010(a(n)), A000010(a(n))<=a(n)+A000203(a(n)); values are odd, see A084821 for odd numbers which are not in the sequence.

Examples

			n=5, a(5)=9: phi(9)=6, sigma(9)=13: (6,9,13)=(A070080(176), A070081(176), A070082(176)).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Divisor Function
• Eric Weisstein's World of Mathematics, Totient Function

Crossrefs

Cf. A046022.

Programs

Mathematica

Select[Range[1, 140, 2], DivisorSigma[1, #] < EulerPhi[#] + # &] (* Amiram Eldar, Sep 12 2019 *)

PARI

is(n)=eulerphi(n)+n>sigma(n) \\ Charles R Greathouse IV, Feb 19 2013