401,024

2⁷ × 13 × 241

401,024 factors as 2^7 × 13 × 241. Its 32 positive divisors give a proper-divisor sum of 462,916, so this integer is abundant. The Collatz stopping time is 130 steps.

Prime Factor Structure

Factorization String 2^7 × 13 × 241

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 863,940

Proper Divisor Sum 462,916

Digit Sum / Digital Root 11 (Root: 2)

Adjacent Primes #401017 ← → #401029

Radix Representation

Decimal	401024
Binary	1100001111010000000 (19 bits)
Octal	0o1417200
Hexadecimal	0x61E80

Divisor Catalog (32)

1 2 4 8 13 16 26 32 52 64 104 128 208 241 416 482 832 964 1,664 1,928 3,133 3,856 6,266 7,712 12,532 15,424 25,064 30,848 50,128 100,256 200,512 401,024

Collatz Trajectory (130 steps to reach 1)

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

401,024 200,512 100,256 50,128 25,064 12,532 6,266 3,133 9,400 4,700 2,350 1,175 3,526 1,763 5,290 2,645 7,936 3,968 1,984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445

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