515,664

2⁴ × 3² × 3581

515,664 factors as 2^4 × 3^2 × 3581. Its 30 positive divisors give a proper-divisor sum of 927,882, so this integer is abundant. The Collatz stopping time is 133 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 3581

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 30

Divisor Sum (σ) 1,443,546

Proper Divisor Sum 927,882

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #515663 ← → #515677

Radix Representation

Decimal	515664
Binary	1111101111001010000 (19 bits)
Octal	0o1757120
Hexadecimal	0x7DE50

Divisor Catalog (30)

1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 3,581 7,162 10,743 14,324 21,486 28,648 32,229 42,972 57,296 64,458 85,944 128,916 171,888 257,832 515,664

Collatz Trajectory (133 steps to reach 1)

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

515,664 257,832 128,916 64,458 32,229 96,688 48,344 24,172 12,086 6,043 18,130 9,065 27,196 13,598 6,799 20,398 10,199 30,598 15,299 45,898 22,949 68,848 34,424 17,212 8,606 4,303 12,910 6,455 19,366 9,683 29,050 14,525 43,576 21,788 10,894 5,447 16,342 8,171 24,514 12,257 36,772 18,386 9,193 27,580 13,790 6,895 20,686 10,343 31,030 15,515 46,546 23,273 69,820 34,910 17,455 52,366 26,183 78,550 39,275 117,826

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