Seventy (70)
1. The sum of divisors of 70 including itself is a square number.
70 has the factors- 1, 2, 5, 7, 10,14, 35 and 70 which when added gives 144 which is a square number. 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144 = 12^2
2. It is the smallest weird number. A number is called weird if it is an abundant number without being the sum of any set of its divisors. As discussed above that 1, 2, 5, 7, 10, 14 , 35 and 70 are the factors of 70 whose sum excluding 70 is 74 but no set of these factors sum to 70.
1 + 2 + 5 + 7 + 10 + 14 + 35 = 74
35 + 14 + 10 + 7 + 5 = 71
35 + 14 + 10 + 7 + 5 = 63
There are very few Weird number and you will be astonished to know that there are only 7 weird number below 10000 and they are 70, 836, 4030, 5830, 7192, 7912 and 9272.
3. The sum of squares of first 24 natural numbers is the square of 70.
1^2 + 2^2 + 3^2 + … + 24^2 = 70^2
4. It is a Pell number. Pell numbers are similar to Fibonacci numbers and are generated by the formula
An = 2 An – 1 + An – 2
The first 10 Pell numbers are 1, 2, 5, 12, 29, 70, 169, 408, 985 and 2378.
5. In base 10 it is a Harshad number as it is divisible by sum of its digit.
6. It is the seventh pentagonal number.
7. The atomic number of Yttterbium is 70.
8. 270 = 1180591620717411303424. The sum of the digits is also 70,
DR RAJESH KUMAR THAKUR
rkthakur1974@gmail.com
1. The sum of divisors of 70 including itself is a square number.
70 has the factors- 1, 2, 5, 7, 10,14, 35 and 70 which when added gives 144 which is a square number. 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144 = 12^2
2. It is the smallest weird number. A number is called weird if it is an abundant number without being the sum of any set of its divisors. As discussed above that 1, 2, 5, 7, 10, 14 , 35 and 70 are the factors of 70 whose sum excluding 70 is 74 but no set of these factors sum to 70.
1 + 2 + 5 + 7 + 10 + 14 + 35 = 74
35 + 14 + 10 + 7 + 5 = 71
35 + 14 + 10 + 7 + 5 = 63
There are very few Weird number and you will be astonished to know that there are only 7 weird number below 10000 and they are 70, 836, 4030, 5830, 7192, 7912 and 9272.
3. The sum of squares of first 24 natural numbers is the square of 70.
1^2 + 2^2 + 3^2 + … + 24^2 = 70^2
4. It is a Pell number. Pell numbers are similar to Fibonacci numbers and are generated by the formula
An = 2 An – 1 + An – 2
The first 10 Pell numbers are 1, 2, 5, 12, 29, 70, 169, 408, 985 and 2378.
5. In base 10 it is a Harshad number as it is divisible by sum of its digit.
6. It is the seventh pentagonal number.
7. The atomic number of Yttterbium is 70.
8. 270 = 1180591620717411303424. The sum of the digits is also 70,
DR RAJESH KUMAR THAKUR
rkthakur1974@gmail.com
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