λ
Harmonic Matrix

5,211,972

22 × 33 × 48259
Abundant Even Composite

5,211,972 has digital root 9. The neighboring primes are 5211959 and 5212003; its proper-divisor sum differs from the starting integer by 3,088,856.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 48259
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 13,512,800
Proper Divisor Sum 8,300,828
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #5211959 ← → #5212003

Radix Representation

Decimal 5211972
Binary 10011111000011101000100 (23 bits)
Octal 0o23703504
Hexadecimal 0x4F8744

Divisor Catalog (24)

1 2 3 4 6 9 12 18 27 36 54 108 48,259 96,518 144,777 193,036 289,554 434,331 579,108 868,662 1,302,993 1,737,324 2,605,986 5,211,972

Collatz Trajectory (188 steps to reach 1)

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

5,211,972 2,605,986 1,302,993 3,908,980 1,954,490 977,245 2,931,736 1,465,868 732,934 366,467 1,099,402 549,701 1,649,104 824,552 412,276 206,138 103,069 309,208 154,604 77,302 38,651 115,954 57,977 173,932 86,966 43,483 130,450 65,225 195,676 97,838 48,919 146,758 73,379 220,138 110,069 330,208 165,104 82,552 41,276 20,638 10,319 30,958 15,479 46,438 23,219 69,658 34,829 104,488 52,244 26,122 13,061 39,184 19,592 9,796 4,898 2,449 7,348 3,674 1,837 5,512

More profiles

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