λ
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Atlas › Integer Profiles › Node 17,528,175

17,528,175

32 × 52 × 7 × 31 × 359
Abundant Odd Composite

17,528,175 factors as 3^2 × 5^2 × 7 × 31 × 359. Its 72 positive divisors give a proper-divisor sum of 19,612,305, so this integer is abundant. The Collatz stopping time is 156 steps.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 7 × 31 × 359
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 37,140,480
Proper Divisor Sum 19,612,305
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #17528149 ← → #17528179

Radix Representation

Decimal 17528175
Binary 1000010110111010101101111 (25 bits)
Octal 0o102672557
Hexadecimal 0x10B756F

Divisor Catalog (60 of 72)

1 3 5 7 9 15 21 25 31 35 45 63 75 93 105 155 175 217 225 279 315 359 465 525 651 775 1,077 1,085 1,395 1,575 1,795 1,953 2,325 2,513 3,231 3,255 5,385 5,425 6,975 7,539 8,975 9,765 11,129 12,565 16,155 16,275 22,617 26,925 33,387 37,695 48,825 55,645 62,825 77,903 80,775 100,161 113,085 166,935 188,475 233,709

Collatz Trajectory (156 steps to reach 1)

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

17,528,175 52,584,526 26,292,263 78,876,790 39,438,395 118,315,186 59,157,593 177,472,780 88,736,390 44,368,195 133,104,586 66,552,293 199,656,880 99,828,440 49,914,220 24,957,110 12,478,555 37,435,666 18,717,833 56,153,500 28,076,750 14,038,375 42,115,126 21,057,563 63,172,690 31,586,345 94,759,036 47,379,518 23,689,759 71,069,278 35,534,639 106,603,918 53,301,959 159,905,878 79,952,939 239,858,818 119,929,409 359,788,228 179,894,114 89,947,057 269,841,172 134,920,586 67,460,293 202,380,880 101,190,440 50,595,220 25,297,610 12,648,805 37,946,416 18,973,208 9,486,604 4,743,302 2,371,651 7,114,954 3,557,477 10,672,432 5,336,216 2,668,108 1,334,054 667,027

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