λ
Harmonic Matrix

6,129,828

22 × 32 × 41 × 4153
Abundant Even Composite

6,129,828 has digital root 9. The neighboring primes are 6129811 and 6129857; its proper-divisor sum differs from the starting integer by 3,616,932.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 41 × 4153
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 15,876,588
Proper Divisor Sum 9,746,760
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #6129811 ← → #6129857

Radix Representation

Decimal 6129828
Binary 10111011000100010100100 (23 bits)
Octal 0o27304244
Hexadecimal 0x5D88A4

Divisor Catalog (36)

1 2 3 4 6 9 12 18 36 41 82 123 164 246 369 492 738 1,476 4,153 8,306 12,459 16,612 24,918 37,377 49,836 74,754 149,508 170,273 340,546 510,819 681,092 1,021,638 1,532,457 2,043,276 3,064,914 6,129,828

Collatz Trajectory (289 steps to reach 1)

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

6,129,828 3,064,914 1,532,457 4,597,372 2,298,686 1,149,343 3,448,030 1,724,015 5,172,046 2,586,023 7,758,070 3,879,035 11,637,106 5,818,553 17,455,660 8,727,830 4,363,915 13,091,746 6,545,873 19,637,620 9,818,810 4,909,405 14,728,216 7,364,108 3,682,054 1,841,027 5,523,082 2,761,541 8,284,624 4,142,312 2,071,156 1,035,578 517,789 1,553,368 776,684 388,342 194,171 582,514 291,257 873,772 436,886 218,443 655,330 327,665 982,996 491,498 245,749 737,248 368,624 184,312 92,156 46,078 23,039 69,118 34,559 103,678 51,839 155,518 77,759 233,278

More profiles

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