λ
Harmonic Matrix

8,763,012

22 × 33 × 41 × 1979
Abundant Even Composite

8,763,012 has digital root 9. The neighboring primes are 8762989 and 8763019; its proper-divisor sum differs from the starting integer by 5,758,776.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 41 × 1979
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 23,284,800
Proper Divisor Sum 14,521,788
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8762989 ← → #8763019

Radix Representation

Decimal 8763012
Binary 100001011011011010000100 (24 bits)
Octal 0o41333204
Hexadecimal 0x85B684

Divisor Catalog (48)

1 2 3 4 6 9 12 18 27 36 41 54 82 108 123 164 246 369 492 738 1,107 1,476 1,979 2,214 3,958 4,428 5,937 7,916 11,874 17,811 23,748 35,622 53,433 71,244 81,139 106,866 162,278 213,732 243,417 324,556 486,834 730,251 973,668 1,460,502 2,190,753 2,921,004 4,381,506 8,763,012

Collatz Trajectory (181 steps to reach 1)

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

8,763,012 4,381,506 2,190,753 6,572,260 3,286,130 1,643,065 4,929,196 2,464,598 1,232,299 3,696,898 1,848,449 5,545,348 2,772,674 1,386,337 4,159,012 2,079,506 1,039,753 3,119,260 1,559,630 779,815 2,339,446 1,169,723 3,509,170 1,754,585 5,263,756 2,631,878 1,315,939 3,947,818 1,973,909 5,921,728 2,960,864 1,480,432 740,216 370,108 185,054 92,527 277,582 138,791 416,374 208,187 624,562 312,281 936,844 468,422 234,211 702,634 351,317 1,053,952 526,976 263,488 131,744 65,872 32,936 16,468 8,234 4,117 12,352 6,176 3,088 1,544

More profiles

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