λ
Harmonic Matrix

5,642,985

3 × 5 × 376199
Deficient Odd Composite

5,642,985 has digital root 3. The neighboring primes are 5642977 and 5642999; its proper-divisor sum differs from the starting integer by -2,257,170.

Prime Factor Structure

Factorization String 3 × 5 × 376199
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 9,028,800
Proper Divisor Sum 3,385,815
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #5642977 ← → #5642999

Radix Representation

Decimal 5642985
Binary 10101100001101011101001 (23 bits)
Octal 0o25415351
Hexadecimal 0x561AE9

Divisor Catalog (8)

1 3 5 15 376,199 1,128,597 1,880,995 5,642,985

Collatz Trajectory (108 steps to reach 1)

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

5,642,985 16,928,956 8,464,478 4,232,239 12,696,718 6,348,359 19,045,078 9,522,539 28,567,618 14,283,809 42,851,428 21,425,714 10,712,857 32,138,572 16,069,286 8,034,643 24,103,930 12,051,965 36,155,896 18,077,948 9,038,974 4,519,487 13,558,462 6,779,231 20,337,694 10,168,847 30,506,542 15,253,271 45,759,814 22,879,907 68,639,722 34,319,861 102,959,584 51,479,792 25,739,896 12,869,948 6,434,974 3,217,487 9,652,462 4,826,231 14,478,694 7,239,347 21,718,042 10,859,021 32,577,064 16,288,532 8,144,266 4,072,133 12,216,400 6,108,200 3,054,100 1,527,050 763,525 2,290,576 1,145,288 572,644 286,322 143,161 429,484 214,742

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