501,150

2 × 3 × 5² × 13 × 257

501,150 factors as 2 × 3 × 5^2 × 13 × 257. Its 48 positive divisors give a proper-divisor sum of 842,514, so this integer is abundant. The Collatz stopping time is 89 steps.

Prime Factor Structure

Factorization String 2 × 3 × 5^2 × 13 × 257

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,343,664

Proper Divisor Sum 842,514

Digit Sum / Digital Root 12 (Root: 3)

Adjacent Primes #501139 ← → #501157

Radix Representation

Decimal	501150
Binary	1111010010110011110 (19 bits)
Octal	0o1722636
Hexadecimal	0x7A59E

Divisor Catalog (48)

1 2 3 5 6 10 13 15 25 26 30 39 50 65 75 78 130 150 195 257 325 390 514 650 771 975 1,285 1,542 1,950 2,570 3,341 3,855 6,425 6,682 7,710 10,023 12,850 16,705 19,275 20,046 33,410 38,550 50,115 83,525 100,230 167,050 250,575 501,150

Collatz Trajectory (89 steps to reach 1)

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

501,150 250,575 751,726 375,863 1,127,590 563,795 1,691,386 845,693 2,537,080 1,268,540 634,270 317,135 951,406 475,703 1,427,110 713,555 2,140,666 1,070,333 3,211,000 1,605,500 802,750 401,375 1,204,126 602,063 1,806,190 903,095 2,709,286 1,354,643 4,063,930 2,031,965 6,095,896 3,047,948 1,523,974 761,987 2,285,962 1,142,981 3,428,944 1,714,472 857,236 428,618 214,309 642,928 321,464 160,732 80,366 40,183 120,550 60,275 180,826 90,413 271,240 135,620 67,810 33,905 101,716 50,858 25,429 76,288 38,144 19,072

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