λ
Harmonic Matrix

692,730

2 × 32 × 5 × 43 × 179
Abundant Even Composite

692,730 has digital root 9. The neighboring primes are 692729 and 692743; its proper-divisor sum differs from the starting integer by 467,820.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 43 × 179
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,853,280
Proper Divisor Sum 1,160,550
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #692729 ← → #692743

Radix Representation

Decimal 692730
Binary 10101001000111111010 (20 bits)
Octal 0o2510772
Hexadecimal 0xA91FA

Divisor Catalog (48)

1 2 3 5 6 9 10 15 18 30 43 45 86 90 129 179 215 258 358 387 430 537 645 774 895 1,074 1,290 1,611 1,790 1,935 2,685 3,222 3,870 5,370 7,697 8,055 15,394 16,110 23,091 38,485 46,182 69,273 76,970 115,455 138,546 230,910 346,365 692,730

Collatz Trajectory (229 steps to reach 1)

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

692,730 346,365 1,039,096 519,548 259,774 129,887 389,662 194,831 584,494 292,247 876,742 438,371 1,315,114 657,557 1,972,672 986,336 493,168 246,584 123,292 61,646 30,823 92,470 46,235 138,706 69,353 208,060 104,030 52,015 156,046 78,023 234,070 117,035 351,106 175,553 526,660 263,330 131,665 394,996 197,498 98,749 296,248 148,124 74,062 37,031 111,094 55,547 166,642 83,321 249,964 124,982 62,491 187,474 93,737 281,212 140,606 70,303 210,910 105,455 316,366 158,183

More profiles

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