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

1,2

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.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A046022.

Sequence in context: A033040 A335241 A200982 * A324846 A324760 A324761

Adjacent sequences: A084817 A084818 A084819 * A084821 A084822 A084823

Keyword

nonn

Author

Reinhard Zumkeller, Jun 04 2003

Status

approved