A070817 a(n) = floor(n/2) - gpf(phi(n)), where gpf(n) is the largest prime factor of n.

-1, 0, 0, 1, 0, 2, 1, 3, 0, 4, 3, 4, 5, 6, 6, 6, 6, 8, 7, 6, 0, 10, 7, 10, 10, 11, 7, 13, 10, 14, 11, 15, 14, 15, 15, 16, 16, 18, 15, 18, 14, 17, 19, 12, 0, 22, 17, 20, 23, 23, 13, 24, 22, 25, 25, 22, 0, 28, 25, 26, 28, 30, 29, 28, 22, 32, 23, 32, 28, 33, 33, 34, 32, 35, 33, 36, 26, 38, 37, 36, 0, 39, 40, 36, 36, 39, 33, 42, 42, 35, 41, 24

Offset

3,6

Links

Table of n, a(n) for n=3..94.

Formula

a(n) = A004526(n) - A068211(n) = A004526(n) - A006530(A000010(n)).

If n is a safe prime, then a(n)=0.

Example

For n=3, floor(3/2) = 1, phi(3) = 2, gpf(2) = 2, a(3) = 1 - 2 = -1.
For n=107, floor(107/2) = 53, phi(107) = 2*53, gpf(106) = 53, a(107) = 53 - 53 = 0.
For n=128, floor(128/2) = 64, gpf(phi(128)) = gpf(64) = 2, a(128) = 64 - 2 = 62.

Mathematica

mf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Table[Floor[n/2//N]-mf[EulerPhi[n]], {w, 3, 128}]

Crossrefs

Cf. A000010, A004526, A005384, A005385, A006530, A068211.

Sequence in context: A208571 A264520 A058208 * A231347 A180988 A127474

Adjacent sequences: A070814 A070815 A070816 * A070818 A070819 A070820

Keyword

easy,sign

Author

Labos Elemer, May 10 2002

Status

approved