82,026

2 × 3³ × 7² × 31

82,026 has digital root 9. The neighboring primes are 82021 and 82031; its proper-divisor sum differs from the starting integer by 54,828.

Prime Factor Structure

Factorization String 2 × 3^3 × 7^2 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 218,880

Proper Divisor Sum 136,854

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #82021 ← → #82031

Radix Representation

Decimal	82026
Binary	10100000001101010 (17 bits)
Octal	0o240152
Hexadecimal	0x1406A

Divisor Catalog (48)

1 2 3 6 7 9 14 18 21 27 31 42 49 54 62 63 93 98 126 147 186 189 217 279 294 378 434 441 558 651 837 882 1,302 1,323 1,519 1,674 1,953 2,646 3,038 3,906 4,557 5,859 9,114 11,718 13,671 27,342 41,013 82,026

Collatz Trajectory (58 steps to reach 1)

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

82,026 41,013 123,040 61,520 30,760 15,380 7,690 3,845 11,536 5,768 2,884 1,442 721 2,164 1,082 541 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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