Harmonic Matrix

9,013,897

113 × 79769

9,013,897 has digital root 1. The neighboring primes are 9013889 and 9013937; its proper-divisor sum differs from the starting integer by -8,934,014.

Prime Factor Structure

Factorization String 113 × 79769

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 4

Divisor Sum (σ) 9,093,780

Proper Divisor Sum 79,883

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #9013889 ← → #9013937

Radix Representation

Decimal	9013897
Binary	100010011000101010001001 (24 bits)
Octal	0o42305211
Hexadecimal	0x898A89

Divisor Catalog (4)

1 113 79,769 9,013,897

Collatz Trajectory (137 steps to reach 1)

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

9,013,897 27,041,692 13,520,846 6,760,423 20,281,270 10,140,635 30,421,906 15,210,953 45,632,860 22,816,430 11,408,215 34,224,646 17,112,323 51,336,970 25,668,485 77,005,456 38,502,728 19,251,364 9,625,682 4,812,841 14,438,524 7,219,262 3,609,631 10,828,894 5,414,447 16,243,342 8,121,671 24,365,014 12,182,507 36,547,522 18,273,761 54,821,284 27,410,642 13,705,321 41,115,964 20,557,982 10,278,991 30,836,974 15,418,487 46,255,462 23,127,731 69,383,194 34,691,597 104,074,792 52,037,396 26,018,698 13,009,349 39,028,048 19,514,024 9,757,012 4,878,506 2,439,253 7,317,760 3,658,880 1,829,440 914,720 457,360 228,680 114,340 57,170

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