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Atlas › Integer Profiles › Node 97,147,288

97,147,288

23 × 7 × 821 × 2113
Abundant Even Composite

97,147,288 factors as 2^3 × 7 × 821 × 2113. Its 32 positive divisors give a proper-divisor sum of 111,377,672, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 821 × 2113
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 208,524,960
Proper Divisor Sum 111,377,672
Digit Sum / Digital Root 46 (Root: 1)
Adjacent Primes #97147249 ← → #97147289

Radix Representation

Decimal 97147288
Binary 101110010100101100110011000 (27 bits)
Octal 0o562454630
Hexadecimal 0x5CA5998

Divisor Catalog (32)

1 2 4 7 8 14 28 56 821 1,642 2,113 3,284 4,226 5,747 6,568 8,452 11,494 14,791 16,904 22,988 29,582 45,976 59,164 118,328 1,734,773 3,469,546 6,939,092 12,143,411 13,878,184 24,286,822 48,573,644 97,147,288

Collatz Trajectory (138 steps to reach 1)

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

97,147,288 48,573,644 24,286,822 12,143,411 36,430,234 18,215,117 54,645,352 27,322,676 13,661,338 6,830,669 20,492,008 10,246,004 5,123,002 2,561,501 7,684,504 3,842,252 1,921,126 960,563 2,881,690 1,440,845 4,322,536 2,161,268 1,080,634 540,317 1,620,952 810,476 405,238 202,619 607,858 303,929 911,788 455,894 227,947 683,842 341,921 1,025,764 512,882 256,441 769,324 384,662 192,331 576,994 288,497 865,492 432,746 216,373 649,120 324,560 162,280 81,140 40,570 20,285 60,856 30,428 15,214 7,607 22,822 11,411 34,234 17,117

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