A220160 -id:A220160 - cp's OEIS frontend

A066232 Numbers k such that phi(k) = phi(k-2) - phi(k-1).

195, 3531, 9339, 27231, 46795, 78183, 90195, 112995, 135015, 437185, 849405, 935221, 1078581, 1283601, 1986975, 2209585, 2341185, 2411175, 2689695, 2744145, 3619071, 3712545, 4738185, 5132985, 6596121, 7829031, 8184715, 12176109

Offset: 1

Joseph L. Pe, Dec 18 2001

nonn

As in A065557, all terms listed here are odd. Problem: Prove that this holds in general.

			Phi(195) = 96 = 192-96 = phi(193)-phi(194).

Harry J. Smith and Jud McCranie, Table of n, a(n) for n = 1..289 (first 55 terms from Harry J. Smith)

Cf. A065557, A066231, A067701, A197112, A220160.

Select[Range[3, 10^6], EulerPhi[ # ] == EulerPhi[ # - 2] - EulerPhi[ # - 1] &]

isok(k) = { k > 2 && eulerphi(k) == eulerphi(k - 2) - eulerphi(k - 1) } \\ Harry J. Smith, Feb 07 2010

a(n) = A220160(n) + 1 = A197112(n) + 2. - Andrew Howroyd, Dec 19 2024

a(13)-a(28) from Harry J. Smith, Feb 07 2010

A076529 Numbers k for which phi(k) = phi(k+1) - phi(k-1).

Original entry on oeis.org

2, 4, 6, 10, 16, 22, 36, 40, 46, 100, 136, 232, 256, 856, 1036, 1296, 1540, 1600, 2016, 4336, 6526, 9178, 14400, 16096, 30496, 55386, 61132, 62800, 65536, 72580, 77616, 110176, 152650, 179296, 244966, 299650, 603460, 619696, 686736, 1876726, 2841916, 3058210

Offset: 1

Joseph L. Pe, Oct 18 2002

nonn

			phi(22) = 10; phi(23) = 22; phi(21) = 12 and 10 = 22 - 12; hence 22 is a term of the sequence.

Donovan Johnson, Table of n, a(n) for n = 1..100

Cf. A000010, A220160.

Select[Range[2, 10^5], EulerPhi[#] == EulerPhi[#+1] - EulerPhi[#-1] &]
Flatten[ Position[Partition[EulerPhi[Range[31*10^5]],3,1],?(#[[2]] == #[[3]] -#[[1]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Dec 28 2017 *)

Missing first term added by Donovan Johnson, Dec 06 2012

A220169 Numbers n for which phi(n^2) = phi(n-1) * phi(n+1).

Original entry on oeis.org

2, 4, 16, 256, 976, 3256, 5188, 11716, 13366, 22936, 65536, 307396, 491536, 589408, 983776, 1659586, 2822716, 3137356, 5577826, 6475456, 7378372, 8698096, 10798726, 32235736, 37797436, 39220126, 39285436, 51555136, 52077196, 56992552, 63767926, 70075996, 82391002

Offset: 1

Carl Najafi, Dec 06 2012

nonn

			phi(976^2) = 468480 = 480*976 = phi(975)*phi(977).

Cf. A000010, A076529, A220160.

Select[Range[10^6], EulerPhi[#^2] == EulerPhi[# - 1] EulerPhi[# + 1] &]

isok(n) = eulerphi(n^2) == eulerphi(n-1) * eulerphi(n+1); \\ Michel Marcus, Aug 12 2019

More terms from Amiram Eldar, Aug 12 2019

cp's OEIS Frontend

A066232 Numbers k such that phi(k) = phi(k-2) - phi(k-1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A076529 Numbers k for which phi(k) = phi(k+1) - phi(k-1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A220169 Numbers n for which phi(n^2) = phi(n-1) * phi(n+1).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions