Find the sum of all the integers N>1 such that the each prime factor of N is

Question

Find the sum of all the integers

N > 1

such that the each prime factor of N is either 2, 3 or 7 and N is not divisible by any perfect cube greater than1.
___

Answer:
:
The number will be of the form

(2^{x}) \times (3^{y}) \times (7^{x})

.
And

0 \leq x, y, z \leq 2

(Since N is not divisible by any perfect cube greater than 1).
Hence sum of all possible combination of numbers is:

(1 + 2 + 4) \times (1 + 3 + 9) \times (1 + 7 + 49) - 1 = 5187 - 1 = 5186

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. Consider the region formed by the intersections of three semi circles whose diameters, of lengths 3, 4 and 5, from a tri....shaded region bounded by the arcs AB, BC and AC?

Question 2. A function f(x) is defined as: f(x) = x15- 2013x14 + 2013x13- 2013x12 + .... - 2013x2 + 2013x. Find the value of f(2012)........ - 2013x2 + 2013x. Find the value of f(2012).

Question 3. Find the sum of 1.1! + 2.2! + 3.3! + ... + (n-1)(n-1)! + n. n!.....

Question 4. Two rugby teams (thirty players) have been selected to play for their school. Five of the players speak Spanish, Afrikaa....one speaks only Spanish. How many players speak only English?

Question 5. Consider the non-decreasing sequence of positive integers: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5.... in which nth ....the remainder when the 2000th term is divided by 4.

Question 6. How many natural number sets of the form Sn={n−4,n−3,n−2,n−1,n,n+1,n+2,n+3,n+4} (n is a natu....does not contain 10 or any integral multiple of 10?

Question 7. In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50-paisa, 25-paisa and 10-paisa coins?....

Question 8. Answer the questions based on the information given below. A microorganism Xeta combines with another microorganism of i....in the same chamber. When will all the Xeta be dead?

Question 9. 2 cows and 7 calves can graze a field in 14 days. 3 cows and 8 calves can graze the same field in 11 days. Then 8 cows a....known that, once grazed; the grass does not grow back

Question 10. Ahmed and Sahil set out together on bicycle traveling at 15 and 12 kilometers per hour, respectively. After 40 minutes, ....hour? (consider Ahmed's deceleration/acceleration before/after the flat to be negligible)

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0