λ
Harmonic Matrix

9,677,320

23 × 5 × 113 × 2141
Abundant Even Composite

9,677,320 has digital root 7. The neighboring primes are 9677309 and 9677321; its proper-divisor sum differs from the starting integer by 2,622,280.

Prime Factor Structure

Factorization String 2^3 × 5 × 113 × 2141
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 21,976,920
Proper Divisor Sum 12,299,600
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #9677309 ← → #9677321

Radix Representation

Decimal 9677320
Binary 100100111010101000001000 (24 bits)
Octal 0o44725010
Hexadecimal 0x93AA08

Divisor Catalog (32)

1 2 4 5 8 10 20 40 113 226 452 565 904 1,130 2,141 2,260 4,282 4,520 8,564 10,705 17,128 21,410 42,820 85,640 241,933 483,866 967,732 1,209,665 1,935,464 2,419,330 4,838,660 9,677,320

Collatz Trajectory (75 steps to reach 1)

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

9,677,320 4,838,660 2,419,330 1,209,665 3,628,996 1,814,498 907,249 2,721,748 1,360,874 680,437 2,041,312 1,020,656 510,328 255,164 127,582 63,791 191,374 95,687 287,062 143,531 430,594 215,297 645,892 322,946 161,473 484,420 242,210 121,105 363,316 181,658 90,829 272,488 136,244 68,122 34,061 102,184 51,092 25,546 12,773 38,320 19,160 9,580 4,790 2,395 7,186 3,593 10,780 5,390 2,695 8,086 4,043 12,130 6,065 18,196 9,098 4,549 13,648 6,824 3,412 1,706

More profiles

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