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Atlas › Integer Profiles › Node 17,528,960

17,528,960

27 × 5 × 61 × 449
Abundant Even Composite

17,528,960 factors as 2^7 × 5 × 61 × 449. Its 64 positive divisors give a proper-divisor sum of 25,158,040, so this integer is abundant. The Collatz stopping time is 89 steps.

Prime Factor Structure

Factorization String 2^7 × 5 × 61 × 449
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 42,687,000
Proper Divisor Sum 25,158,040
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #17528957 ← → #17528971

Radix Representation

Decimal 17528960
Binary 1000010110111100010000000 (25 bits)
Octal 0o102674200
Hexadecimal 0x10B7880

Divisor Catalog (60 of 64)

1 2 4 5 8 10 16 20 32 40 61 64 80 122 128 160 244 305 320 449 488 610 640 898 976 1,220 1,796 1,952 2,245 2,440 3,592 3,904 4,490 4,880 7,184 7,808 8,980 9,760 14,368 17,960 19,520 27,389 28,736 35,920 39,040 54,778 57,472 71,840 109,556 136,945 143,680 219,112 273,890 287,360 438,224 547,780 876,448 1,095,560 1,752,896 2,191,120

Collatz Trajectory (89 steps to reach 1)

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

17,528,960 8,764,480 4,382,240 2,191,120 1,095,560 547,780 273,890 136,945 410,836 205,418 102,709 308,128 154,064 77,032 38,516 19,258 9,629 28,888 14,444 7,222 3,611 10,834 5,417 16,252 8,126 4,063 12,190 6,095 18,286 9,143 27,430 13,715 41,146 20,573 61,720 30,860 15,430 7,715 23,146 11,573 34,720 17,360 8,680 4,340 2,170 1,085 3,256 1,628 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86

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