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2,467,647

32 × 7 × 13 × 23 × 131
Deficient Odd Composite

2,467,647 factors as 3^2 × 7 × 13 × 23 × 131. Its 48 positive divisors give a proper-divisor sum of 2,144,961, so this integer is deficient. The Collatz stopping time is 205 steps.

Prime Factor Structure

Factorization String 3^2 × 7 × 13 × 23 × 131
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 4,612,608
Proper Divisor Sum 2,144,961
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #2467643 ← → #2467649

Radix Representation

Decimal 2467647
Binary 1001011010011100111111 (22 bits)
Octal 0o11323477
Hexadecimal 0x25A73F

Divisor Catalog (48)

1 3 7 9 13 21 23 39 63 69 91 117 131 161 207 273 299 393 483 819 897 917 1,179 1,449 1,703 2,093 2,691 2,751 3,013 5,109 6,279 8,253 9,039 11,921 15,327 18,837 21,091 27,117 35,763 39,169 63,273 107,289 117,507 189,819 274,183 352,521 822,549 2,467,647

Collatz Trajectory (205 steps to reach 1)

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

2,467,647 7,402,942 3,701,471 11,104,414 5,552,207 16,656,622 8,328,311 24,984,934 12,492,467 37,477,402 18,738,701 56,216,104 28,108,052 14,054,026 7,027,013 21,081,040 10,540,520 5,270,260 2,635,130 1,317,565 3,952,696 1,976,348 988,174 494,087 1,482,262 741,131 2,223,394 1,111,697 3,335,092 1,667,546 833,773 2,501,320 1,250,660 625,330 312,665 937,996 468,998 234,499 703,498 351,749 1,055,248 527,624 263,812 131,906 65,953 197,860 98,930 49,465 148,396 74,198 37,099 111,298 55,649 166,948 83,474 41,737 125,212 62,606 31,303 93,910

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