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Atlas › Integer Profiles › Node 83,037,834

83,037,834

2 × 32 × 11 × 419383
Abundant Even Composite

83,037,834 factors as 2 × 3^2 × 11 × 419383. Its 24 positive divisors give a proper-divisor sum of 113,233,878, so this integer is abundant. The Collatz stopping time is 179 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 11 × 419383
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 196,271,712
Proper Divisor Sum 113,233,878
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #83037827 ← → #83037853

Radix Representation

Decimal 83037834
Binary 100111100110000111010001010 (27 bits)
Octal 0o474607212
Hexadecimal 0x4F30E8A

Divisor Catalog (24)

1 2 3 6 9 11 18 22 33 66 99 198 419,383 838,766 1,258,149 2,516,298 3,774,447 4,613,213 7,548,894 9,226,426 13,839,639 27,679,278 41,518,917 83,037,834

Collatz Trajectory (179 steps to reach 1)

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

83,037,834 41,518,917 124,556,752 62,278,376 31,139,188 15,569,594 7,784,797 23,354,392 11,677,196 5,838,598 2,919,299 8,757,898 4,378,949 13,136,848 6,568,424 3,284,212 1,642,106 821,053 2,463,160 1,231,580 615,790 307,895 923,686 461,843 1,385,530 692,765 2,078,296 1,039,148 519,574 259,787 779,362 389,681 1,169,044 584,522 292,261 876,784 438,392 219,196 109,598 54,799 164,398 82,199 246,598 123,299 369,898 184,949 554,848 277,424 138,712 69,356 34,678 17,339 52,018 26,009 78,028 39,014 19,507 58,522 29,261 87,784

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