λ
Prime Ledger

85,839

3 × 13 × 31 × 71
Deficient Odd Composite

85,839 has the prime decomposition 3 × 13 × 31 × 71. Its 4 distinct prime factors produce 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 13 × 31 × 71
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 129,024
Proper Divisor Sum 43,185
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #85837 ← → #85843

Radix Representation

Decimal 85839
Binary 10100111101001111 (17 bits)
Octal 0o247517
Hexadecimal 0x14F4F

Divisor Catalog (16)

1 3 13 31 39 71 93 213 403 923 1,209 2,201 2,769 6,603 28,613 85,839

Collatz Trajectory (151 steps to reach 1)

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

85,839 257,518 128,759 386,278 193,139 579,418 289,709 869,128 434,564 217,282 108,641 325,924 162,962 81,481 244,444 122,222 61,111 183,334 91,667 275,002 137,501 412,504 206,252 103,126 51,563 154,690 77,345 232,036 116,018 58,009 174,028 87,014 43,507 130,522 65,261 195,784 97,892 48,946 24,473 73,420 36,710 18,355 55,066 27,533 82,600 41,300 20,650 10,325 30,976 15,488 7,744 3,872 1,936 968 484 242 121 364 182 91

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