6174 (number)

6174
6174
	six thousand one hundred seventy four
← 6172 · 6173 · 6174 · 6175 · 6176 →
Factorization	2 · 3 2 · 7 3
Roman notation	V MCLXXIV
Binary	1100000011110
Octal	14036
Hexadecimal	181E

6174 ( six thousand one hundred seventy four ) is a natural number located between the numbers 6173 and 6175, the constant of Caprecar .

Content

1 Math
- 1.1 Kaprekara constant
- 1.2 Other properties
2 notes
3 Literature
4 References

Math

6174 is an even four-digit number.

Kaprekara constant

The number 6174 is the Caprecar constant ^[1] for four-digit numbers.

Other properties

6174 is the number of harshad ^[2] , since it is divided by the sum of its numbers:

6174 = (6 + 1 + 7 + 4) × 343.

6174 is a practical number , since any number less than 6174 can be represented as the sum of different divisors of 6174 ^[2] ^[3] . The nearest numbers with this property are 6160, 6162, 6180, 6188 ^[3] ^[4] . In addition, 6174 is the Zumkeller number , since the set of divisors of 6174 can be divided into two subsets with equal sums (7800) ^[2] ^[5] .

There is no natural number, dividing by the sum of its digits it turns out 6174 ^[2] ^[6] . The nearest numbers with this property are 6123, 6150, 6185, 6189 ^[7] .

The number 6174 can be represented as the sum of the first three natural degrees of the number 18 ^[8] :

18 ³ + 18 ² + 18 ¹ = 5832 + 324 + 18 = 6174.

The sum of the squares of the prime factors of 6174 is the exact square ^[9] :

2 ² + 3 ² + 3 ² + 7 ² + 7 ² + 7 ² = 4 + 9 + 9 + 49 + 49 + 49 = 169 = 13 ² .

Notes

↑ David Wells. 6174 // The Penguin Dictionary of Curious and Interesting Numbers . - 1st ed. - Penguin Books , 1987 .-- 229 p. - ISBN 0-14-008029-5 .
↑ ¹ ² ³ ⁴ 6174: facts & properties (neopr.) . Numbers Aplenty: interesting natural numbers and their properties.
↑ ¹ ² Tanya Khovanova. 6174 (neopr.) . Number Gossip.
↑ Sequence A005153 in OEIS = Practical numbers: positive integers n such that every k <= sigma (n) is a sum of distinct divisors of n. Also called panarithmic numbers.
↑ A083207 sequence in OEIS = Zumkeller numbers: numbers n whose divisors can be partitioned into two disjoint sets whose sums are both sigma (n) / 2 // Fragment: 6162, 6168, 6174 , 6180, 6186
↑ inconsummate numbers (neopr.) . Numbers Aplenty.
↑ A003635 sequence in OEIS = Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10)
↑ Sequence A027444 in OEIS = a (n) = n ^ 3 + n ^ 2 + n
↑ A134605 sequence in OEIS = Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer

Literature

. 6174 // Les nombres remarquables (French) . - , 1983. - ISBN 2705614079 .
GrrlScientist. 6174 (Kaprekar's Constant) (neopr.) (December 12, 2011).

Links

Number 6174 in OEIS
Yutaka Nishiyama. Mysterious number 6174 (neopr.) . plus.maths.org (March 1, 2006).

[wells-1] David Wells. 6174 // The Penguin Dictionary of Curious and Interesting Numbers . - 1st ed. - Penguin Books , 1987 .-- 229 p. - ISBN 0-14-008029-5 .

[nap-2] ¹ ² ³ ⁴ 6174: facts & properties (neopr.) . Numbers Aplenty: interesting natural numbers and their properties.

[gossip-3] ¹ ² Tanya Khovanova. 6174 (neopr.) . Number Gossip.

[4] Sequence A005153 in OEIS = Practical numbers: positive integers n such that every k <= sigma (n) is a sum of distinct divisors of n. Also called panarithmic numbers.

[5] A083207 sequence in OEIS = Zumkeller numbers: numbers n whose divisors can be partitioned into two disjoint sets whose sums are both sigma (n) / 2 // Fragment: 6162, 6168, 6174 , 6180, 6186

[6] summate numbers (neopr.) . Numbers Aplenty.

[7] A003635 sequence in OEIS = Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10)

[8] Sequence A027444 in OEIS = a (n) = n ^ 3 + n ^ 2 + n

[9] A134605 sequence in OEIS = Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer