How to resolve the algorithm Chowla numbers step by step in the PicoLisp programming language

Published on 12 May 2024 09:40 PM
#Picolisp

How to resolve the algorithm Chowla numbers step by step in the PicoLisp programming language

Table of Contents

Problem Statement

Chowla numbers are also known as:

The chowla number of   n   is   (as defined by Chowla's function):

The sequence is named after   Sarvadaman D. S. Chowla,   (22 October 1907 ──► 10 December 1995), a London born Indian American mathematician specializing in number theory.

German mathematician Carl Friedrich Gauss (1777─1855) said:

Chowla numbers can also be expressed as:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Chowla numbers step by step in the PicoLisp programming language

Source code in the picolisp programming language

(de accu1 (Var Key)
   (if (assoc Key (val Var))
      (con @ (inc (cdr @)))
      (push Var (cons Key 1)) )
   Key )
(de factor (N)
   (let
      (R NIL
         D 2
         L (1 2 2 . (4 2 4 2 4 6 2 6 .))
         M (sqrt N) )
      (while (>= M D)
         (if (=0 (% N D))
            (setq M
               (sqrt (setq N (/ N (accu1 'R D)))) )
            (inc 'D (pop 'L)) ) )
      (accu1 'R N)
      (mapcar
         '((L)
            (make
               (for N (cdr L)
                  (link (** (car L) N)) ) ) )
         R ) ) )
(de chowla (N)
   (let F (factor N)
      (-
         (sum
            prog
            (make
               (link 1)
               (mapc
                  '((A)
                     (chain
                        (mapcan
                           '((B)
                              (mapcar '((C) (* C B)) (made)) )
                           A ) ) )
                  F ) ) )
         N
         1 ) ) )
(de prime (N)
   (and (> N 1) (=0 (chowla N))) )
(de perfect (N)
   (and
      (> N 1)
      (= (chowla N) (dec N))) )
(de countP (N)
   (let C 0
      (for I N
         (and (prime I) (inc 'C)) )
      C ) )
(de listP (N)
   (make
      (for I N
         (and (perfect I) (link I)) ) ) )
(for I 37
   (prinl "chowla(" I ") = " (chowla I)) )
(prinl "Count of primes up to      100 = " (countP 100))
(prinl "Count of primes up to     1000 = " (countP 1000))
(prinl "Count of primes up to    10000 = " (countP 10000))
(prinl "Count of primes up to   100000 = " (countP 100000))
(prinl "Count of primes up to  1000000 = " (countP 1000000))
(prinl "Count of primes up to 10000000 = " (countP 10000000))
(println (listP 35000000))

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