A066232 -id:A066232 - cp's OEIS frontend

A066231 Numbers n such that phi(n) = phi(n-1) - phi(n-2).

6, 8, 26, 78, 218, 306, 3666, 4646, 5066, 8816, 12206, 12546, 19878, 20436, 24236, 29546, 37736, 47996, 60116, 72086, 73026, 77046, 87476, 121146, 126056, 129246, 149756, 190268, 234636, 247856, 273296, 275724, 419366, 531236, 553476, 621726

Offset: 1

Joseph L. Pe, Dec 18 2001

nonn

Question: Are all terms of this sequence even? (Compare A065557, whose terms could be all odd and squarefree.)

			phi(8) = 4 = 6-2 = phi(7) - phi(6).

Harry J. Smith and Jud McCranie, Table of n, a(n) for n = 1..494 (first 117 terms from Harry J. Smith)

Cf. A066232, A067701.

Flatten[Position[Partition[EulerPhi[Range[630000]],3,1],?(#[[3]] == #[[2]]- #[[1]]&),1,Heads->False]]+2 (* _Harvey P. Dale, Aug 19 2018 *)

n=0; for (m=3, 10^9, if (eulerphi(m) == eulerphi(m - 1) - eulerphi(m - 2), write("b066231.txt", n++, " ", m); if (n==117, return)) ) \\ Harry J. Smith, Feb 06 2010

a(24)-a(36) from Harry J. Smith, Feb 06 2010

A197112 Numbers k such that phi(k) = phi(k+1) + phi(k+2).

Original entry on oeis.org

193, 3529, 9337, 27229, 46793, 78181, 90193, 112993, 135013, 437183, 849403, 935219, 1078579, 1283599, 1986973, 2209583, 2341183, 2411173, 2689693, 2744143, 3619069, 3712543, 4738183, 5132983, 6596119, 7829029, 8184713

Offset: 1

Antonio Roldán, Oct 10 2011

nonn

For k less than 4*10^6, k is prime, semiprime, or triprime (3-almost prime).

			112993 is in the sequence, because phi(112993) = 106704, phi(112994) = 48384, phi(112995) = 58320  and 106704 = 48384 + 58320.

Amiram Eldar, Table of n, a(n) for n = 1..289 (calculated using the b-file at A066232)

Cf. A000010, A066232, A092404.

for k from 0 do
        if numtheory[phi](k) = numtheory[phi](k+1)+numtheory[phi](k+2) then
                printf("%d\n",k) ;
        end if;
end do: # R. J. Mathar, Oct 13 2011

Select[Range[10^5], EulerPhi[#] == EulerPhi[# + 1] + EulerPhi[# + 2] &] (* Alonso del Arte, Oct 13 2011 *)
Position[Partition[EulerPhi[Range[82*10^5]],3,1],?(#[[1]]==#[[2]]+#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 10 2022 *)

isok(n) = eulerphi(n) == eulerphi(n+1) + eulerphi(n+2); \\ Michel Marcus, May 15 2016

a(n) = A066232(n)-2. - Donovan Johnson, Oct 14 2011

a(27) from Vincenzo Librandi, Sep 27 2013

A066359 Nonsquarefree numbers n such that phi(n) = phi(n-2)-phi(n-1), where phi is Euler's totient function.

Original entry on oeis.org

46795, 78183, 112995, 1986975, 2411175, 2689695, 2744145, 3619071, 3712545, 4738185, 8184715, 12176109, 13342959, 26400843, 33789015, 40425645, 61114185, 78464475, 83333565, 167077575, 212066541, 248682015, 326834725, 336828205, 353707705, 391078425, 880254585

Offset: 1

Jason Earls, Dec 20 2001

nonn

See comment in A066232.

Numbers in A066232 that are not squarefree.

ph1=1; ph2=1; for(n=3, 880254585, ph3=eulerphi(n); if(issquarefree(n)==0, if(ph3==ph1-ph2, print1(n ", "))); ph1=ph2; ph2=ph3) /* Donovan Johnson, Oct 20 2012 */

a(10)-a(27) from Donovan Johnson, Oct 20 2012

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A066231 Numbers n such that phi(n) = phi(n-1) - phi(n-2).

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A197112 Numbers k such that phi(k) = phi(k+1) + phi(k+2).

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A066359 Nonsquarefree numbers n such that phi(n) = phi(n-2)-phi(n-1), where phi is Euler's totient function.

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