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Atlas › Integer Profiles › Node 30,157,728

30,157,728

25 × 3 × 172 × 1087
Abundant Even Composite

30,157,728 factors as 2^5 × 3 × 17^2 × 1087. Its 72 positive divisors give a proper-divisor sum of 54,014,304, so this integer is abundant. The Collatz stopping time is 175 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 17^2 × 1087
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 84,172,032
Proper Divisor Sum 54,014,304
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #30157727 ← → #30157789

Radix Representation

Decimal 30157728
Binary 1110011000010101110100000 (25 bits)
Octal 0o163025640
Hexadecimal 0x1CC2BA0

Divisor Catalog (60 of 72)

1 2 3 4 6 8 12 16 17 24 32 34 48 51 68 96 102 136 204 272 289 408 544 578 816 867 1,087 1,156 1,632 1,734 2,174 2,312 3,261 3,468 4,348 4,624 6,522 6,936 8,696 9,248 13,044 13,872 17,392 18,479 26,088 27,744 34,784 36,958 52,176 55,437 73,916 104,352 110,874 147,832 221,748 295,664 314,143 443,496 591,328 628,286

Collatz Trajectory (175 steps to reach 1)

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

30,157,728 15,078,864 7,539,432 3,769,716 1,884,858 942,429 2,827,288 1,413,644 706,822 353,411 1,060,234 530,117 1,590,352 795,176 397,588 198,794 99,397 298,192 149,096 74,548 37,274 18,637 55,912 27,956 13,978 6,989 20,968 10,484 5,242 2,621 7,864 3,932 1,966 983 2,950 1,475 4,426 2,213 6,640 3,320 1,660 830 415 1,246 623 1,870 935 2,806 1,403 4,210 2,105 6,316 3,158 1,579 4,738 2,369 7,108 3,554 1,777 5,332

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