A070002 Numbers k such that phi(P(k)) - P(phi(k)) = 1, where P(k) is the largest prime factor of k.

45, 90, 135, 175, 180, 270, 350, 360, 405, 525, 540, 700, 720, 810, 875, 1050, 1080, 1215, 1400, 1440, 1573, 1575, 1620, 1750, 2100, 2160, 2430, 2625, 2800, 2880, 3146, 3150, 3240, 3500, 3645, 4200, 4320, 4375, 4719, 4725, 4860, 5250, 5491, 5600, 5760

Offset

1,1

Comments

phi(P(k)) - P(phi(k)) = A000010(A006530(k)) - A006530(A000010(k)) = 1, where P(k) = largest prime factor of k. Value of commutator of phi and P functions at k equals 1.

Many but not all terms are divisible by 5.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

m = 77077 = 7*7*11*11*13*13 is here because P(m) = 13, phi(P(13)) = 12, phi(m) = 55440 = 2*2*2*2*3*3*5*7*11 with P(Phi(55440)) = 13 and the difference is 13 - 12 = 1.

Mathematica

pf[n_] := FactorInteger[n][[-1, 1]];
Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 1], Print[n]], {n, 3, 100000}]

Crossrefs

Cf. A000010, A006530, A068211, A070777, A070812, A070003, A070004, A007283, A070813, A070814, A070815, A070816.

Sequence in context: A184540 A115827 A389459 * A101794 A124017 A121925

Adjacent sequences: A069999 A070000 A070001 * A070003 A070004 A070005

Keyword

nonn

Author

Labos Elemer, May 07 2002

Status

approved