How to resolve the algorithm Sequence: nth number with exactly n divisors step by step in the ALGOL 68 programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Sequence: nth number with exactly n divisors step by step in the ALGOL 68 programming language
Table of Contents
Problem Statement
Calculate the sequence where each term an is the nth that has n divisors. Show here, on this page, at least the first 15 terms of the sequence.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Sequence: nth number with exactly n divisors step by step in the ALGOL 68 programming language
Source code in the algol programming language
BEGIN
INT max number = 500 000; # maximum number we will count the divisors of #
# form a table of proper divisor counts #
[ 1 : max number ]INT pdc; FOR i TO UPB pdc DO pdc[ i ] := 1 OD;
pdc[ 1 ] := 0;
FOR i FROM 2 TO UPB pdc DO
FOR j FROM i + i BY i TO UPB pdc DO pdc[ j ] +:= 1 OD
OD;
# find the first few primes #
[ 1 : 30 ]INT prime;
INT p count := 0;
FOR i WHILE p count < UPB prime DO
IF pdc[ i ] = 1 THEN prime[ p count +:= 1 ] := i FI
OD;
# show the nth number with n divisors #
INT w = -43; # width to print the numbers (negative means no leading +) #
print( ( " 1: ", whole( 1, w ), " | 1", newline ) );
FOR i FROM 2 TO 23 DO
print( ( whole( i, -2 ), ": " ) );
IF pdc( i ) = 1 THEN
print( ( whole( LENG LENG prime[ i ] ^ ( i - 1 ), w ), newline ) )
ELSE
INT c := 0;
FOR j TO UPB pdc WHILE c < i DO
IF pdc[ j ] = i - 1 THEN
c +:= 1;
IF c = i THEN
print( ( whole( j, w ), " | 1" ) );
FOR d FROM 2 TO j OVER 2 DO
IF j MOD d = 0 THEN print( ( " ", whole( d, 0 ) ) ) FI
OD;
print( ( " ", whole( j, 0 ), newline ) )
FI
FI
OD
FI
OD
END
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