λ
Harmonic Matrix

5,727,940

22 × 5 × 286397
Abundant Even Composite

5,727,940 has digital root 7. The neighboring primes are 5727923 and 5727971; its proper-divisor sum differs from the starting integer by 572,836.

Prime Factor Structure

Factorization String 2^2 × 5 × 286397
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 12,028,716
Proper Divisor Sum 6,300,776
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #5727923 ← → #5727971

Radix Representation

Decimal 5727940
Binary 10101110110011011000100 (23 bits)
Octal 0o25663304
Hexadecimal 0x5766C4

Divisor Catalog (12)

1 2 4 5 10 20 286,397 572,794 1,145,588 1,431,985 2,863,970 5,727,940

Collatz Trajectory (126 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

5,727,940 2,863,970 1,431,985 4,295,956 2,147,978 1,073,989 3,221,968 1,610,984 805,492 402,746 201,373 604,120 302,060 151,030 75,515 226,546 113,273 339,820 169,910 84,955 254,866 127,433 382,300 191,150 95,575 286,726 143,363 430,090 215,045 645,136 322,568 161,284 80,642 40,321 120,964 60,482 30,241 90,724 45,362 22,681 68,044 34,022 17,011 51,034 25,517 76,552 38,276 19,138 9,569 28,708 14,354 7,177 21,532 10,766 5,383 16,150 8,075 24,226 12,113 36,340

More profiles

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