λ
Harmonic Matrix

8,315,964

22 × 32 × 230999
Abundant Even Composite

8,315,964 has digital root 9. The neighboring primes are 8315927 and 8315969; its proper-divisor sum differs from the starting integer by 4,389,072.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 230999
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 18
Divisor Sum (σ) 21,021,000
Proper Divisor Sum 12,705,036
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8315927 ← → #8315969

Radix Representation

Decimal 8315964
Binary 11111101110010000111100 (23 bits)
Octal 0o37562074
Hexadecimal 0x7EE43C

Divisor Catalog (18)

1 2 3 4 6 9 12 18 36 230,999 461,998 692,997 923,996 1,385,994 2,078,991 2,771,988 4,157,982 8,315,964

Collatz Trajectory (168 steps to reach 1)

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

8,315,964 4,157,982 2,078,991 6,236,974 3,118,487 9,355,462 4,677,731 14,033,194 7,016,597 21,049,792 10,524,896 5,262,448 2,631,224 1,315,612 657,806 328,903 986,710 493,355 1,480,066 740,033 2,220,100 1,110,050 555,025 1,665,076 832,538 416,269 1,248,808 624,404 312,202 156,101 468,304 234,152 117,076 58,538 29,269 87,808 43,904 21,952 10,976 5,488 2,744 1,372 686 343 1,030 515 1,546 773 2,320 1,160 580 290 145 436 218 109 328 164 82 41

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