The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A084820 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

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.
(history; published version)

#10 by Alois P. Heinz at Thu Sep 12 10:36:32 EDT 2019

STATUS

proposed

approved

#9 by Amiram Eldar at Thu Sep 12 10:31:36 EDT 2019

STATUS

editing

proposed

#8 by Amiram Eldar at Thu Sep 12 10:20:14 EDT 2019

LINKS

Amiram Eldar, <a href="/A084820/b084820.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

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

STATUS

approved

editing

#7 by Charles R Greathouse IV at Tue Feb 19 04:48:32 EST 2013

STATUS

editing

approved

#6 by Charles R Greathouse IV at Tue Feb 19 04:48:27 EST 2013

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function.</a>

PROG

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

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:50:35 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Jun 04 2003

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

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.

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Jun 04 2003

#2 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

NAME

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

EXAMPLE

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

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

NAME

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

DATA

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

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function.</a>

EXAMPLE

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

CROSSREFS

Cf. A046022.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 04 2003

STATUS

approved