λ
Harmonic Matrix

8,998,011

32 × 11 × 97 × 937
Deficient Odd Composite

8,998,011 has digital root 9. The neighboring primes are 8997979 and 8998061; its proper-divisor sum differs from the starting integer by -3,655,878.

Prime Factor Structure

Factorization String 3^2 × 11 × 97 × 937
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 14,340,144
Proper Divisor Sum 5,342,133
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8997979 ← → #8998061

Radix Representation

Decimal 8998011
Binary 100010010100110001111011 (24 bits)
Octal 0o42246173
Hexadecimal 0x894C7B

Divisor Catalog (24)

1 3 9 11 33 97 99 291 873 937 1,067 2,811 3,201 8,433 9,603 10,307 30,921 90,889 92,763 272,667 818,001 999,779 2,999,337 8,998,011

Collatz Trajectory (111 steps to reach 1)

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

8,998,011 26,994,034 13,497,017 40,491,052 20,245,526 10,122,763 30,368,290 15,184,145 45,552,436 22,776,218 11,388,109 34,164,328 17,082,164 8,541,082 4,270,541 12,811,624 6,405,812 3,202,906 1,601,453 4,804,360 2,402,180 1,201,090 600,545 1,801,636 900,818 450,409 1,351,228 675,614 337,807 1,013,422 506,711 1,520,134 760,067 2,280,202 1,140,101 3,420,304 1,710,152 855,076 427,538 213,769 641,308 320,654 160,327 480,982 240,491 721,474 360,737 1,082,212 541,106 270,553 811,660 405,830 202,915 608,746 304,373 913,120 456,560 228,280 114,140 57,070

More profiles

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