λ
Harmonic Matrix

4,827,174

2 × 3 × 112 × 61 × 109
Abundant Even Composite

4,827,174 has digital root 6. The neighboring primes are 4827169 and 4827191; its proper-divisor sum differs from the starting integer by 1,230,372.

Prime Factor Structure

Factorization String 2 × 3 × 11^2 × 61 × 109
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 10,884,720
Proper Divisor Sum 6,057,546
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #4827169 ← → #4827191

Radix Representation

Decimal 4827174
Binary 10010011010100000100110 (23 bits)
Octal 0o22324046
Hexadecimal 0x49A826

Divisor Catalog (48)

1 2 3 6 11 22 33 61 66 109 121 122 183 218 242 327 363 366 654 671 726 1,199 1,342 2,013 2,398 3,597 4,026 6,649 7,194 7,381 13,189 13,298 14,762 19,947 22,143 26,378 39,567 39,894 44,286 73,139 79,134 146,278 219,417 438,834 804,529 1,609,058 2,413,587 4,827,174

Collatz Trajectory (113 steps to reach 1)

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

4,827,174 2,413,587 7,240,762 3,620,381 10,861,144 5,430,572 2,715,286 1,357,643 4,072,930 2,036,465 6,109,396 3,054,698 1,527,349 4,582,048 2,291,024 1,145,512 572,756 286,378 143,189 429,568 214,784 107,392 53,696 26,848 13,424 6,712 3,356 1,678 839 2,518 1,259 3,778 1,889 5,668 2,834 1,417 4,252 2,126 1,063 3,190 1,595 4,786 2,393 7,180 3,590 1,795 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569 1,708 854

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