λ
Harmonic Matrix

9,120,215

5 × 13 × 193 × 727
Deficient Odd Composite

9,120,215 has digital root 2. The neighboring primes are 9120203 and 9120217; its proper-divisor sum differs from the starting integer by -6,376,942.

Prime Factor Structure

Factorization String 5 × 13 × 193 × 727
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 11,863,488
Proper Divisor Sum 2,743,273
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #9120203 ← → #9120217

Radix Representation

Decimal 9120215
Binary 100010110010100111010111 (24 bits)
Octal 0o42624727
Hexadecimal 0x8B29D7

Divisor Catalog (16)

1 5 13 65 193 727 965 2,509 3,635 9,451 12,545 47,255 140,311 701,555 1,824,043 9,120,215

Collatz Trajectory (163 steps to reach 1)

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

9,120,215 27,360,646 13,680,323 41,040,970 20,520,485 61,561,456 30,780,728 15,390,364 7,695,182 3,847,591 11,542,774 5,771,387 17,314,162 8,657,081 25,971,244 12,985,622 6,492,811 19,478,434 9,739,217 29,217,652 14,608,826 7,304,413 21,913,240 10,956,620 5,478,310 2,739,155 8,217,466 4,108,733 12,326,200 6,163,100 3,081,550 1,540,775 4,622,326 2,311,163 6,933,490 3,466,745 10,400,236 5,200,118 2,600,059 7,800,178 3,900,089 11,700,268 5,850,134 2,925,067 8,775,202 4,387,601 13,162,804 6,581,402 3,290,701 9,872,104 4,936,052 2,468,026 1,234,013 3,702,040 1,851,020 925,510 462,755 1,388,266 694,133 2,082,400

More profiles

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