λ
Harmonic Matrix

2,716,720

24 × 5 × 29 × 1171
Abundant Even Composite

2,716,720 has digital root 7. The neighboring primes are 2716711 and 2716729; its proper-divisor sum differs from the starting integer by 1,106,320.

Prime Factor Structure

Factorization String 2^4 × 5 × 29 × 1171
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 6,539,760
Proper Divisor Sum 3,823,040
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #2716711 ← → #2716729

Radix Representation

Decimal 2716720
Binary 1010010111010000110000 (22 bits)
Octal 0o12272060
Hexadecimal 0x297430

Divisor Catalog (40)

1 2 4 5 8 10 16 20 29 40 58 80 116 145 232 290 464 580 1,160 1,171 2,320 2,342 4,684 5,855 9,368 11,710 18,736 23,420 33,959 46,840 67,918 93,680 135,836 169,795 271,672 339,590 543,344 679,180 1,358,360 2,716,720

Collatz Trajectory (156 steps to reach 1)

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

2,716,720 1,358,360 679,180 339,590 169,795 509,386 254,693 764,080 382,040 191,020 95,510 47,755 143,266 71,633 214,900 107,450 53,725 161,176 80,588 40,294 20,147 60,442 30,221 90,664 45,332 22,666 11,333 34,000 17,000 8,500 4,250 2,125 6,376 3,188 1,594 797 2,392 1,196 598 299 898 449 1,348 674 337 1,012 506 253 760 380 190 95 286 143 430 215 646 323 970 485

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