λ
Harmonic Matrix

7,142,210

2 × 5 × 17 × 42013
Deficient Even Composite

7,142,210 has digital root 8. The neighboring primes are 7142209 and 7142263; its proper-divisor sum differs from the starting integer by -671,884.

Prime Factor Structure

Factorization String 2 × 5 × 17 × 42013
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 13,612,536
Proper Divisor Sum 6,470,326
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #7142209 ← → #7142263

Radix Representation

Decimal 7142210
Binary 11011001111101101000010 (23 bits)
Octal 0o33175502
Hexadecimal 0x6CFB42

Divisor Catalog (16)

1 2 5 10 17 34 85 170 42,013 84,026 210,065 420,130 714,221 1,428,442 3,571,105 7,142,210

Collatz Trajectory (160 steps to reach 1)

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

7,142,210 3,571,105 10,713,316 5,356,658 2,678,329 8,034,988 4,017,494 2,008,747 6,026,242 3,013,121 9,039,364 4,519,682 2,259,841 6,779,524 3,389,762 1,694,881 5,084,644 2,542,322 1,271,161 3,813,484 1,906,742 953,371 2,860,114 1,430,057 4,290,172 2,145,086 1,072,543 3,217,630 1,608,815 4,826,446 2,413,223 7,239,670 3,619,835 10,859,506 5,429,753 16,289,260 8,144,630 4,072,315 12,216,946 6,108,473 18,325,420 9,162,710 4,581,355 13,744,066 6,872,033 20,616,100 10,308,050 5,154,025 15,462,076 7,731,038 3,865,519 11,596,558 5,798,279 17,394,838 8,697,419 26,092,258 13,046,129 39,138,388 19,569,194 9,784,597

More profiles

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