λ
Harmonic Matrix

1,170,880

26 × 5 × 3659
Abundant Even Composite

1,170,880 has digital root 7. The neighboring primes are 1170863 and 1170899; its proper-divisor sum differs from the starting integer by 447,160.

Prime Factor Structure

Factorization String 2^6 × 5 × 3659
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 2,788,920
Proper Divisor Sum 1,618,040
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #1170863 ← → #1170899

Radix Representation

Decimal 1170880
Binary 100011101110111000000 (21 bits)
Octal 0o4356700
Hexadecimal 0x11DDC0

Divisor Catalog (28)

1 2 4 5 8 10 16 20 32 40 64 80 160 320 3,659 7,318 14,636 18,295 29,272 36,590 58,544 73,180 117,088 146,360 234,176 292,720 585,440 1,170,880

Collatz Trajectory (72 steps to reach 1)

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

1,170,880 585,440 292,720 146,360 73,180 36,590 18,295 54,886 27,443 82,330 41,165 123,496 61,748 30,874 15,437 46,312 23,156 11,578 5,789 17,368 8,684 4,342 2,171 6,514 3,257 9,772 4,886 2,443 7,330 3,665 10,996 5,498 2,749 8,248 4,124 2,062 1,031 3,094 1,547 4,642 2,321 6,964 3,482 1,741 5,224 2,612 1,306 653 1,960 980 490 245 736 368 184 92 46 23 70 35

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