A073462 Number of solutions to phi(x) - pi(x) = n.

6, 8, 5, 9, 3, 3, 6, 6, 1, 5, 5, 3, 3, 5, 3, 4, 6, 1, 5, 7, 5, 2, 4, 2, 1, 5, 5, 1, 4, 2, 2, 7, 3, 4, 4, 4, 2, 5, 1, 4, 1, 6, 4, 5, 3, 2, 4, 2, 3, 6, 1, 6, 3, 6, 3, 1, 1, 2, 5, 4, 3, 3, 4, 2, 0, 4, 3, 4, 3, 1, 2, 6, 4, 4, 0, 5, 5, 4, 2, 6, 4, 3, 2, 5, 5, 1, 1, 9, 1, 3, 1, 4, 4, 3, 3, 2, 4, 4, 3, 2, 4

Offset

-1,1

Comments

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

Links

Table of n, a(n) for n=-1..99.

Formula

a(n)=Card[{x; A000010(x)-A000720(x)=n}]

Example

n=-1: 6 solutions = {6,12,18,24,42,60}, a(-1)=6; n=5: for 6 terms of {11,32,34,50,70,150}, phi(#) - pi(#) = 6 holds, so a(5)=6; n=63: no solution was found at x <= 1000000.

Crossrefs

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

Sequence in context: A030644 A319032 A344125 * A231095 A201195 A266092

Adjacent sequences: A073459 A073460 A073461 * A073463 A073464 A073465

Keyword

nonn

Author

Labos Elemer, Aug 02 2002

Status

approved