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Atlas › Integer Profiles › Node 36,769,068

36,769,068

22 × 32 × 7 × 53 × 2753
Abundant Even Composite

36,769,068 factors as 2^2 × 3^2 × 7 × 53 × 2753. Its 72 positive divisors give a proper-divisor sum of 71,496,180, so this integer is abundant. The Collatz stopping time is 183 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 7 × 53 × 2753
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 108,265,248
Proper Divisor Sum 71,496,180
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #36769067 ← → #36769081

Radix Representation

Decimal 36769068
Binary 10001100010000110100101100 (26 bits)
Octal 0o214206454
Hexadecimal 0x2310D2C

Divisor Catalog (60 of 72)

1 2 3 4 6 7 9 12 14 18 21 28 36 42 53 63 84 106 126 159 212 252 318 371 477 636 742 954 1,113 1,484 1,908 2,226 2,753 3,339 4,452 5,506 6,678 8,259 11,012 13,356 16,518 19,271 24,777 33,036 38,542 49,554 57,813 77,084 99,108 115,626 145,909 173,439 231,252 291,818 346,878 437,727 583,636 693,756 875,454 1,021,363

Collatz Trajectory (183 steps to reach 1)

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

36,769,068 18,384,534 9,192,267 27,576,802 13,788,401 41,365,204 20,682,602 10,341,301 31,023,904 15,511,952 7,755,976 3,877,988 1,938,994 969,497 2,908,492 1,454,246 727,123 2,181,370 1,090,685 3,272,056 1,636,028 818,014 409,007 1,227,022 613,511 1,840,534 920,267 2,760,802 1,380,401 4,141,204 2,070,602 1,035,301 3,105,904 1,552,952 776,476 388,238 194,119 582,358 291,179 873,538 436,769 1,310,308 655,154 327,577 982,732 491,366 245,683 737,050 368,525 1,105,576 552,788 276,394 138,197 414,592 207,296 103,648 51,824 25,912 12,956 6,478

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