The Museum of HP Calculators

# Euler Function for the HP-65

This program is Copyright © 1974 by Hewlett-Packard and is used here by permission. This program was originally published in the HP-65 Math Pac 2.

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

 Euler Function Jn(x) Label (n) Key A B C D E

## Overview

(n) is the number of integers not exceeding and relatively prime to n, where n is a non-negative integer.

Suppose

n = p1m1p2m2. . . pkmk

where Pi (i = 1, 2, ..., k) are distinct primes dividing n, then

(n) = n i=1..k(1-1/pi)

= i=1..k(pimi - pimi-1)

## Instructions

 Step Instructions Input Data/Units Keys Output Data/Units 1 Enter Program 2 n A (n)

## Examples

1. (30) = 8.00
2. (251) = 250.00

## The Program

``` CODE  KEYS
23  LBL
11  A
33 01  STO 1
01  1
33 02  STO 2
33 04  STO 4
02  2
33 03  STO 3

23  LBL
01  1
34 01  RCL 1
34 03  RCL 3
81  ÷
34 03  RCL 3
35 24  g x>y
22  GTO
02  2
35 08  g roll dn
31  f
83  INT
35 00  g LST X
35 24  g x>y
22  GTO
03  3
33 01  STO 1
34 04  RCL 4
34 03  RCL 3
33 04  STO 4
35 21  g x!=y
01  1
51  -
33  STO
71  x
02  2
22  GTO
01  1

23  LBL
03  3
02  2
34 03  RCL 3
35 23  g x=y
44  CLX
01  1
61  +
33 03  STO 3
22  GTO
01  1

23  LBL
02  2
34 04  RCL 4
34 01  RCL 1
35 21  g x!=y
01  1
51  -
34 02  RCL 2
71  x
24  RTN
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
```

## Register Use

```R1  used
R2  used
R3  used
R4  used
R5
R6
R7
R8
R9  used
```