λ
Harmonic Matrix

3,715,326

2 × 32 × 206407
Abundant Even Composite

3,715,326 has digital root 9. The neighboring primes are 3715307 and 3715343; its proper-divisor sum differs from the starting integer by 619,260.

Prime Factor Structure

Factorization String 2 × 3^2 × 206407
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 8,049,912
Proper Divisor Sum 4,334,586
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #3715307 ← → #3715343

Radix Representation

Decimal 3715326
Binary 1110001011000011111110 (22 bits)
Octal 0o16130376
Hexadecimal 0x38B0FE

Divisor Catalog (12)

1 2 3 6 9 18 206,407 412,814 619,221 1,238,442 1,857,663 3,715,326

Collatz Trajectory (340 steps to reach 1)

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

3,715,326 1,857,663 5,572,990 2,786,495 8,359,486 4,179,743 12,539,230 6,269,615 18,808,846 9,404,423 28,213,270 14,106,635 42,319,906 21,159,953 63,479,860 31,739,930 15,869,965 47,609,896 23,804,948 11,902,474 5,951,237 17,853,712 8,926,856 4,463,428 2,231,714 1,115,857 3,347,572 1,673,786 836,893 2,510,680 1,255,340 627,670 313,835 941,506 470,753 1,412,260 706,130 353,065 1,059,196 529,598 264,799 794,398 397,199 1,191,598 595,799 1,787,398 893,699 2,681,098 1,340,549 4,021,648 2,010,824 1,005,412 502,706 251,353 754,060 377,030 188,515 565,546 282,773 848,320

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