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Atlas › Integer Profiles › Node 29,222,752

29,222,752

25 × 13 × 199 × 353
Abundant Even Composite

29,222,752 factors as 2^5 × 13 × 199 × 353. Its 48 positive divisors give a proper-divisor sum of 33,222,848, so this integer is abundant. The Collatz stopping time is 206 steps.

Prime Factor Structure

Factorization String 2^5 × 13 × 199 × 353
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 62,445,600
Proper Divisor Sum 33,222,848
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #29222747 ← → #29222771

Radix Representation

Decimal 29222752
Binary 1101111011110011101100000 (25 bits)
Octal 0o157363540
Hexadecimal 0x1BDE760

Divisor Catalog (48)

1 2 4 8 13 16 26 32 52 104 199 208 353 398 416 706 796 1,412 1,592 2,587 2,824 3,184 4,589 5,174 5,648 6,368 9,178 10,348 11,296 18,356 20,696 36,712 41,392 70,247 73,424 82,784 140,494 146,848 280,988 561,976 913,211 1,123,952 1,826,422 2,247,904 3,652,844 7,305,688 14,611,376 29,222,752

Collatz Trajectory (206 steps to reach 1)

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

29,222,752 14,611,376 7,305,688 3,652,844 1,826,422 913,211 2,739,634 1,369,817 4,109,452 2,054,726 1,027,363 3,082,090 1,541,045 4,623,136 2,311,568 1,155,784 577,892 288,946 144,473 433,420 216,710 108,355 325,066 162,533 487,600 243,800 121,900 60,950 30,475 91,426 45,713 137,140 68,570 34,285 102,856 51,428 25,714 12,857 38,572 19,286 9,643 28,930 14,465 43,396 21,698 10,849 32,548 16,274 8,137 24,412 12,206 6,103 18,310 9,155 27,466 13,733 41,200 20,600 10,300 5,150

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