172,641

3 × 7 × 8221

For 172,641, the 8 positive divisors have a total of 263,104. Removing 172,641 leaves 90,463, which gives the deficient classification.

Prime Factor Structure

Factorization String 3 × 7 × 8221

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 263,104

Proper Divisor Sum 90,463

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #172633 ← → #172643

Radix Representation

Decimal	172641
Binary	101010001001100001 (18 bits)
Octal	0o521141
Hexadecimal	0x2A261

Divisor Catalog (8)

1 3 7 21 8,221 24,663 57,547 172,641

Collatz Trajectory (196 steps to reach 1)

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

172,641 517,924 258,962 129,481 388,444 194,222 97,111 291,334 145,667 437,002 218,501 655,504 327,752 163,876 81,938 40,969 122,908 61,454 30,727 92,182 46,091 138,274 69,137 207,412 103,706 51,853 155,560 77,780 38,890 19,445 58,336 29,168 14,584 7,292 3,646 1,823 5,470 2,735 8,206 4,103 12,310 6,155 18,466 9,233 27,700 13,850 6,925 20,776 10,388 5,194 2,597 7,792 3,896 1,948 974 487 1,462 731 2,194 1,097

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