A066198 Numbers n where phi changes as fast as sigma, i.e., abs(phi(n+1) - phi(n)) = abs(sigma(n+1) - sigma(n)).

2, 6, 8, 10, 22, 46, 58, 82, 106, 166, 178, 188, 226, 262, 285, 346, 358, 382, 466, 478, 502, 562, 586, 718, 838, 854, 862, 886, 902, 982, 1018, 1186, 1282, 1306, 1318, 1366, 1438, 1486, 1522, 1618, 1822, 1906, 2013, 2026, 2038, 2062, 2098, 2206, 2446, 2458

Offset: 1

Author

Joseph L. Pe, Dec 16 2001

Keywords

• nonn

Comments

This sequence is the union of two sequences A145748 and A145749. See comment lines of A145749. [Farideh Firoozbakht, Nov 01 2008]

Examples

			|phi(7) - phi(6)| = |6 - 2| = |8 - 12| = |sigma(7) - sigma(6)|.
|phi(9) - phi(8)| = |6 - 4| = 2 = |13 - 15| = |sigma(9) - sigma(8)|.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065387, A145748, A145749.

Programs

Mathematica

Select[ Range[ 1, 10^4 ], Abs[ DivisorSigma[ 1, # + 1 ] - DivisorSigma[ 1, # ] ] == Abs[ EulerPhi[ # + 1 ] - EulerPhi[ # ] ] & ]

PARI

{ n=0; for (m=1, 10^9, if (abs(eulerphi(m + 1) - eulerphi(m)) == abs(sigma(m + 1) - sigma(m)), write("b066198.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 05 2010

Extensions

More terms from Jason Earls, Jun 05 2002