λ
Harmonic Matrix

5,760,150

2 × 3 × 52 × 11 × 3491
Abundant Even Composite

5,760,150 has digital root 6. The neighboring primes are 5760137 and 5760163; its proper-divisor sum differs from the starting integer by 4,067,988.

Prime Factor Structure

Factorization String 2 × 3 × 5^2 × 11 × 3491
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 15,588,288
Proper Divisor Sum 9,828,138
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #5760137 ← → #5760163

Radix Representation

Decimal 5760150
Binary 10101111110010010010110 (23 bits)
Octal 0o25762226
Hexadecimal 0x57E496

Divisor Catalog (48)

1 2 3 5 6 10 11 15 22 25 30 33 50 55 66 75 110 150 165 275 330 550 825 1,650 3,491 6,982 10,473 17,455 20,946 34,910 38,401 52,365 76,802 87,275 104,730 115,203 174,550 192,005 230,406 261,825 384,010 523,650 576,015 960,025 1,152,030 1,920,050 2,880,075 5,760,150

Collatz Trajectory (121 steps to reach 1)

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

5,760,150 2,880,075 8,640,226 4,320,113 12,960,340 6,480,170 3,240,085 9,720,256 4,860,128 2,430,064 1,215,032 607,516 303,758 151,879 455,638 227,819 683,458 341,729 1,025,188 512,594 256,297 768,892 384,446 192,223 576,670 288,335 865,006 432,503 1,297,510 648,755 1,946,266 973,133 2,919,400 1,459,700 729,850 364,925 1,094,776 547,388 273,694 136,847 410,542 205,271 615,814 307,907 923,722 461,861 1,385,584 692,792 346,396 173,198 86,599 259,798 129,899 389,698 194,849 584,548 292,274 146,137 438,412 219,206

More profiles

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