A073461 Largest solution to phi(x) - pi(x) = n or 0 if no such solution exists.

30, 60, 90, 84, 210, 78, 72, 150, 126, 180, 132, 80, 168, 138, 240, 68, 330, 420, 174, 162, 300, 390, 92, 234, 294, 228, 360, 222, 116, 246, 118, 336, 630, 510, 312, 450, 378, 288, 480, 280, 318, 77, 660, 260, 324, 396, 546, 540, 840, 372, 504, 408, 350, 600

Offset

-2,1

Comments

Although pi takes all values, solutions are not guaranteed since nontotient numbers exist.

a(63) does not exist since by bounds on phi and pi, phi(x) - pi(x) > 129 > 63 for x > 2000 and no smaller x yields a difference of 63. [Charles R Greathouse IV, Oct 31 2011]

Links

Table of n, a(n) for n=-2..51.

Formula

a(n) = Max{x: A000010(x) - A000720(x) = n}

Example

n=92: phi(92)=44, pi(92)=24, a(44-24)=a(20)=92; n=63: no solution was found at x<=1000000.
a(-2) = 30, since phi(30) - pi(30) = 8 - 10 = -2.

Mathematica

Function[s, Function[t, Take[#, 54] &@ ReplacePart[t, Map[# + 3 -> Lookup[s, #][[-1]] &, Keys@ s]]]@ ConstantArray[0, Max@ Keys@ s + 3]]@ KeySort@ PositionIndex@ Array[EulerPhi@ # - PrimePi@ # &, 10^5] (* Michael De Vlieger, Jul 20 2017 *)

Crossrefs

Cf. A000010, A000720, A037228, A037171, A073453-A073457, A072530, A072531, A073461, A073462.

Sequence in context: A221054 A365795 A074915 * A377259 A222618 A325992

Adjacent sequences: A073458 A073459 A073460 * A073462 A073463 A073464

Keyword

nonn

Author

Labos Elemer, Aug 02 2002

Extensions

a(-2) added by Michael De Vlieger, Jul 21 2017

Status

approved