Problem 2674. Generalised Hamming Number

Created by Jean-Marie Sainthillier

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Inspired by Project Euler n°204 and Problem 1308 by James

A generalised Hamming number of type n, has no prime factor larger than n.

For example a generalised Hamming number of type 5 has no prime factor larger than 5.

Given a number X, determine how many generalised Hamming numbers n are less than or equal to that number. Please note that 1 counts as a Hamming number.

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Last Solution submitted on Nov 16, 2025

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Jonathan on 20 Nov 2014

I like your test suite. Using large X forces a better solution.

Jean-Marie Sainthillier on 20 Nov 2014

Thank you Jonathan. I have discovered this philosophy thanks to James and @bmtran problems.

Asif Newaz on 25 Dec 2019

is there any mathematical algorithm that i dont know about to calculate such big range(10^13)?
i minimized my code as best as i can.still fails for such large number.

Nguyen Minh Dat on 13 Aug 2021

why i can't submit my solutions

Hoang Minh Tri 11 hours and 16 minutes ago

thuật toán sinh số nhé các em yêu khóa sau nếu chẳng may gặp thầy Hiệp

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Problem 2674. Generalised Hamming Number

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Problem 2674. Generalised Hamming Number

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Last 200 Solutions

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Solution Comments

Problem Recent Solvers351

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