λ
Harmonic Matrix

700,060

22 × 5 × 17 × 29 × 71
Abundant Even Composite

700,060 has digital root 4. The neighboring primes are 700057 and 700067; its proper-divisor sum differs from the starting integer by 232,840.

Prime Factor Structure

Factorization String 2^2 × 5 × 17 × 29 × 71
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,632,960
Proper Divisor Sum 932,900
Digit Sum / Digital Root 13 (Root: 4)
Adjacent Primes #700057 ← → #700067

Radix Representation

Decimal 700060
Binary 10101010111010011100 (20 bits)
Octal 0o2527234
Hexadecimal 0xAAE9C

Divisor Catalog (48)

1 2 4 5 10 17 20 29 34 58 68 71 85 116 142 145 170 284 290 340 355 493 580 710 986 1,207 1,420 1,972 2,059 2,414 2,465 4,118 4,828 4,930 6,035 8,236 9,860 10,295 12,070 20,590 24,140 35,003 41,180 70,006 140,012 175,015 350,030 700,060

Collatz Trajectory (154 steps to reach 1)

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

700,060 350,030 175,015 525,046 262,523 787,570 393,785 1,181,356 590,678 295,339 886,018 443,009 1,329,028 664,514 332,257 996,772 498,386 249,193 747,580 373,790 186,895 560,686 280,343 841,030 420,515 1,261,546 630,773 1,892,320 946,160 473,080 236,540 118,270 59,135 177,406 88,703 266,110 133,055 399,166 199,583 598,750 299,375 898,126 449,063 1,347,190 673,595 2,020,786 1,010,393 3,031,180 1,515,590 757,795 2,273,386 1,136,693 3,410,080 1,705,040 852,520 426,260 213,130 106,565 319,696 159,848

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