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Atlas › Integer Profiles › Node 33,744,192

33,744,192

26 × 3 × 181 × 971
Abundant Even Composite

33,744,192 factors as 2^6 × 3 × 181 × 971. Its 56 positive divisors give a proper-divisor sum of 56,123,040, so this integer is abundant. The Collatz stopping time is 131 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 181 × 971
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 89,867,232
Proper Divisor Sum 56,123,040
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #33744149 ← → #33744203

Radix Representation

Decimal 33744192
Binary 10000000101110010101000000 (26 bits)
Octal 0o200562500
Hexadecimal 0x202E540

Divisor Catalog (56)

1 2 3 4 6 8 12 16 24 32 48 64 96 181 192 362 543 724 971 1,086 1,448 1,942 2,172 2,896 2,913 3,884 4,344 5,792 5,826 7,768 8,688 11,584 11,652 15,536 17,376 23,304 31,072 34,752 46,608 62,144 93,216 175,751 186,432 351,502 527,253 703,004 1,054,506 1,406,008 2,109,012 2,812,016 4,218,024 5,624,032 8,436,048 11,248,064 16,872,096 33,744,192

Collatz Trajectory (131 steps to reach 1)

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

33,744,192 16,872,096 8,436,048 4,218,024 2,109,012 1,054,506 527,253 1,581,760 790,880 395,440 197,720 98,860 49,430 24,715 74,146 37,073 111,220 55,610 27,805 83,416 41,708 20,854 10,427 31,282 15,641 46,924 23,462 11,731 35,194 17,597 52,792 26,396 13,198 6,599 19,798 9,899 29,698 14,849 44,548 22,274 11,137 33,412 16,706 8,353 25,060 12,530 6,265 18,796 9,398 4,699 14,098 7,049 21,148 10,574 5,287 15,862 7,931 23,794 11,897 35,692

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