λ
Harmonic Matrix

1,533,804

22 × 3 × 127817
Abundant Even Composite

1,533,804 has digital root 6. The neighboring primes are 1533799 and 1533809; its proper-divisor sum differs from the starting integer by 511,296.

Prime Factor Structure

Factorization String 2^2 × 3 × 127817
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 3,578,904
Proper Divisor Sum 2,045,100
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #1533799 ← → #1533809

Radix Representation

Decimal 1533804
Binary 101110110011101101100 (21 bits)
Octal 0o5663554
Hexadecimal 0x17676C

Divisor Catalog (12)

1 2 3 4 6 12 127,817 255,634 383,451 511,268 766,902 1,533,804

Collatz Trajectory (101 steps to reach 1)

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

1,533,804 766,902 383,451 1,150,354 575,177 1,725,532 862,766 431,383 1,294,150 647,075 1,941,226 970,613 2,911,840 1,455,920 727,960 363,980 181,990 90,995 272,986 136,493 409,480 204,740 102,370 51,185 153,556 76,778 38,389 115,168 57,584 28,792 14,396 7,198 3,599 10,798 5,399 16,198 8,099 24,298 12,149 36,448 18,224 9,112 4,556 2,278 1,139 3,418 1,709 5,128 2,564 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271

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