λ
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Atlas › Integer Profiles › Node 29,581,936

29,581,936

24 × 19 × 31 × 43 × 73
Abundant Even Composite

29,581,936 factors as 2^4 × 19 × 31 × 43 × 73. Its 80 positive divisors give a proper-divisor sum of 35,017,104, so this integer is abundant. The Collatz stopping time is 87 steps.

Prime Factor Structure

Factorization String 2^4 × 19 × 31 × 43 × 73
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 64,599,040
Proper Divisor Sum 35,017,104
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #29581927 ← → #29581939

Radix Representation

Decimal 29581936
Binary 1110000110110001001110000 (25 bits)
Octal 0o160661160
Hexadecimal 0x1C36270

Divisor Catalog (60 of 80)

1 2 4 8 16 19 31 38 43 62 73 76 86 124 146 152 172 248 292 304 344 496 584 589 688 817 1,168 1,178 1,333 1,387 1,634 2,263 2,356 2,666 2,774 3,139 3,268 4,526 4,712 5,332 5,548 6,278 6,536 9,052 9,424 10,664 11,096 12,556 13,072 18,104 21,328 22,192 25,112 25,327 36,208 42,997 50,224 50,654 59,641 85,994

Collatz Trajectory (87 steps to reach 1)

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

29,581,936 14,790,968 7,395,484 3,697,742 1,848,871 5,546,614 2,773,307 8,319,922 4,159,961 12,479,884 6,239,942 3,119,971 9,359,914 4,679,957 14,039,872 7,019,936 3,509,968 1,754,984 877,492 438,746 219,373 658,120 329,060 164,530 82,265 246,796 123,398 61,699 185,098 92,549 277,648 138,824 69,412 34,706 17,353 52,060 26,030 13,015 39,046 19,523 58,570 29,285 87,856 43,928 21,964 10,982 5,491 16,474 8,237 24,712 12,356 6,178 3,089 9,268 4,634 2,317 6,952 3,476 1,738 869

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