λ
Harmonic Matrix

2,078,916

22 × 3 × 7 × 24749
Abundant Even Composite

2,078,916 has digital root 6. The neighboring primes are 2078887 and 2078917; its proper-divisor sum differs from the starting integer by 1,386,168.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 24749
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 5,544,000
Proper Divisor Sum 3,465,084
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #2078887 ← → #2078917

Radix Representation

Decimal 2078916
Binary 111111011100011000100 (21 bits)
Octal 0o7734304
Hexadecimal 0x1FB8C4

Divisor Catalog (24)

1 2 3 4 6 7 12 14 21 28 42 84 24,749 49,498 74,247 98,996 148,494 173,243 296,988 346,486 519,729 692,972 1,039,458 2,078,916

Collatz Trajectory (135 steps to reach 1)

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

2,078,916 1,039,458 519,729 1,559,188 779,594 389,797 1,169,392 584,696 292,348 146,174 73,087 219,262 109,631 328,894 164,447 493,342 246,671 740,014 370,007 1,110,022 555,011 1,665,034 832,517 2,497,552 1,248,776 624,388 312,194 156,097 468,292 234,146 117,073 351,220 175,610 87,805 263,416 131,708 65,854 32,927 98,782 49,391 148,174 74,087 222,262 111,131 333,394 166,697 500,092 250,046 125,023 375,070 187,535 562,606 281,303 843,910 421,955 1,265,866 632,933 1,898,800 949,400 474,700

More profiles

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