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Atlas › Integer Profiles › Node 17,527,794

17,527,794

2 × 3 × 23 × 157 × 809
Abundant Even Composite

17,527,794 factors as 2 × 3 × 23 × 157 × 809. Its 32 positive divisors give a proper-divisor sum of 19,330,446, so this integer is abundant. The Collatz stopping time is 200 steps.

Prime Factor Structure

Factorization String 2 × 3 × 23 × 157 × 809
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 36,858,240
Proper Divisor Sum 19,330,446
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #17527793 ← → #17527813

Radix Representation

Decimal 17527794
Binary 1000010110111001111110010 (25 bits)
Octal 0o102671762
Hexadecimal 0x10B73F2

Divisor Catalog (32)

1 2 3 6 23 46 69 138 157 314 471 809 942 1,618 2,427 3,611 4,854 7,222 10,833 18,607 21,666 37,214 55,821 111,642 127,013 254,026 381,039 762,078 2,921,299 5,842,598 8,763,897 17,527,794

Collatz Trajectory (200 steps to reach 1)

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

17,527,794 8,763,897 26,291,692 13,145,846 6,572,923 19,718,770 9,859,385 29,578,156 14,789,078 7,394,539 22,183,618 11,091,809 33,275,428 16,637,714 8,318,857 24,956,572 12,478,286 6,239,143 18,717,430 9,358,715 28,076,146 14,038,073 42,114,220 21,057,110 10,528,555 31,585,666 15,792,833 47,378,500 23,689,250 11,844,625 35,533,876 17,766,938 8,883,469 26,650,408 13,325,204 6,662,602 3,331,301 9,993,904 4,996,952 2,498,476 1,249,238 624,619 1,873,858 936,929 2,810,788 1,405,394 702,697 2,108,092 1,054,046 527,023 1,581,070 790,535 2,371,606 1,185,803 3,557,410 1,778,705 5,336,116 2,668,058 1,334,029 4,002,088

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