λ
Harmonic Matrix

2,187,647

7 × 11 × 28411
Deficient Odd Composite

2,187,647 has digital root 8. The neighboring primes are 2187629 and 2187667; its proper-divisor sum differs from the starting integer by -1,647,742.

Prime Factor Structure

Factorization String 7 × 11 × 28411
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 2,727,552
Proper Divisor Sum 539,905
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #2187629 ← → #2187667

Radix Representation

Decimal 2187647
Binary 1000010110000101111111 (22 bits)
Octal 0o10260577
Hexadecimal 0x21617F

Divisor Catalog (8)

1 7 11 77 28,411 198,877 312,521 2,187,647

Collatz Trajectory (241 steps to reach 1)

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

2,187,647 6,562,942 3,281,471 9,844,414 4,922,207 14,766,622 7,383,311 22,149,934 11,074,967 33,224,902 16,612,451 49,837,354 24,918,677 74,756,032 37,378,016 18,689,008 9,344,504 4,672,252 2,336,126 1,168,063 3,504,190 1,752,095 5,256,286 2,628,143 7,884,430 3,942,215 11,826,646 5,913,323 17,739,970 8,869,985 26,609,956 13,304,978 6,652,489 19,957,468 9,978,734 4,989,367 14,968,102 7,484,051 22,452,154 11,226,077 33,678,232 16,839,116 8,419,558 4,209,779 12,629,338 6,314,669 18,944,008 9,472,004 4,736,002 2,368,001 7,104,004 3,552,002 1,776,001 5,328,004 2,664,002 1,332,001 3,996,004 1,998,002 999,001 2,997,004

More profiles

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