λ
Harmonic Matrix

3,277,710

2 × 32 × 5 × 79 × 461
Abundant Even Composite

3,277,710 has digital root 9. The neighboring primes are 3277699 and 3277721; its proper-divisor sum differs from the starting integer by 2,093,220.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 79 × 461
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 8,648,640
Proper Divisor Sum 5,370,930
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #3277699 ← → #3277721

Radix Representation

Decimal 3277710
Binary 1100100000001110001110 (22 bits)
Octal 0o14401616
Hexadecimal 0x32038E

Divisor Catalog (48)

1 2 3 5 6 9 10 15 18 30 45 79 90 158 237 395 461 474 711 790 922 1,185 1,383 1,422 2,305 2,370 2,766 3,555 4,149 4,610 6,915 7,110 8,298 13,830 20,745 36,419 41,490 72,838 109,257 182,095 218,514 327,771 364,190 546,285 655,542 1,092,570 1,638,855 3,277,710

Collatz Trajectory (89 steps to reach 1)

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

3,277,710 1,638,855 4,916,566 2,458,283 7,374,850 3,687,425 11,062,276 5,531,138 2,765,569 8,296,708 4,148,354 2,074,177 6,222,532 3,111,266 1,555,633 4,666,900 2,333,450 1,166,725 3,500,176 1,750,088 875,044 437,522 218,761 656,284 328,142 164,071 492,214 246,107 738,322 369,161 1,107,484 553,742 276,871 830,614 415,307 1,245,922 622,961 1,868,884 934,442 467,221 1,401,664 700,832 350,416 175,208 87,604 43,802 21,901 65,704 32,852 16,426 8,213 24,640 12,320 6,160 3,080 1,540 770 385 1,156 578

More profiles

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