Euler Function for the HP-65 (original) (raw)

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Card Labels

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

Overview

Φ(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

Φ(n) = n Πi=1..k(1-1/pi)

= Πi=1..k(pimi - pimi-1)

Instructions

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

Examples

1. Φ(30) = 8.00
2. Φ(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 R↓ 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 × 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 × 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

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