λ
Harmonic Matrix

8,721,892

22 × 53 × 41141
Deficient Even Composite

8,721,892 has digital root 1. The neighboring primes are 8721883 and 8721907; its proper-divisor sum differs from the starting integer by -1,892,108.

Prime Factor Structure

Factorization String 2^2 × 53 × 41141
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 15,551,676
Proper Divisor Sum 6,829,784
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #8721883 ← → #8721907

Radix Representation

Decimal 8721892
Binary 100001010001010111100100 (24 bits)
Octal 0o41212744
Hexadecimal 0x8515E4

Divisor Catalog (12)

1 2 4 53 106 212 41,141 82,282 164,564 2,180,473 4,360,946 8,721,892

Collatz Trajectory (124 steps to reach 1)

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

8,721,892 4,360,946 2,180,473 6,541,420 3,270,710 1,635,355 4,906,066 2,453,033 7,359,100 3,679,550 1,839,775 5,519,326 2,759,663 8,278,990 4,139,495 12,418,486 6,209,243 18,627,730 9,313,865 27,941,596 13,970,798 6,985,399 20,956,198 10,478,099 31,434,298 15,717,149 47,151,448 23,575,724 11,787,862 5,893,931 17,681,794 8,840,897 26,522,692 13,261,346 6,630,673 19,892,020 9,946,010 4,973,005 14,919,016 7,459,508 3,729,754 1,864,877 5,594,632 2,797,316 1,398,658 699,329 2,097,988 1,048,994 524,497 1,573,492 786,746 393,373 1,180,120 590,060 295,030 147,515 442,546 221,273 663,820 331,910

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