λ
Harmonic Matrix

9,988,470

2 × 32 × 5 × 29 × 43 × 89
Abundant Even Composite

9,988,470 has digital root 9. The neighboring primes are 9988453 and 9988481; its proper-divisor sum differs from the starting integer by 7,822,260.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 29 × 43 × 89
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 96
Divisor Sum (σ) 27,799,200
Proper Divisor Sum 17,810,730
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #9988453 ← → #9988481

Radix Representation

Decimal 9988470
Binary 100110000110100101110110 (24 bits)
Octal 0o46064566
Hexadecimal 0x986976

Divisor Catalog (60 of 96)

1 2 3 5 6 9 10 15 18 29 30 43 45 58 86 87 89 90 129 145 174 178 215 258 261 267 290 387 430 435 445 522 534 645 774 801 870 890 1,247 1,290 1,305 1,335 1,602 1,935 2,494 2,581 2,610 2,670 3,741 3,827 3,870 4,005 5,162 6,235 7,482 7,654 7,743 8,010 11,223 11,481

Collatz Trajectory (137 steps to reach 1)

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

9,988,470 4,994,235 14,982,706 7,491,353 22,474,060 11,237,030 5,618,515 16,855,546 8,427,773 25,283,320 12,641,660 6,320,830 3,160,415 9,481,246 4,740,623 14,221,870 7,110,935 21,332,806 10,666,403 31,999,210 15,999,605 47,998,816 23,999,408 11,999,704 5,999,852 2,999,926 1,499,963 4,499,890 2,249,945 6,749,836 3,374,918 1,687,459 5,062,378 2,531,189 7,593,568 3,796,784 1,898,392 949,196 474,598 237,299 711,898 355,949 1,067,848 533,924 266,962 133,481 400,444 200,222 100,111 300,334 150,167 450,502 225,251 675,754 337,877 1,013,632 506,816 253,408 126,704 63,352

More profiles

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