λ
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Atlas › Integer Profiles › Node 57,740,540

57,740,540

22 × 5 × 11 × 132 × 1553
Abundant Even Composite

57,740,540 factors as 2^2 × 5 × 11 × 13^2 × 1553. Its 72 positive divisors give a proper-divisor sum of 85,587,988, so this integer is abundant. The Collatz stopping time is 269 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 11 × 13^2 × 1553
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 143,328,528
Proper Divisor Sum 85,587,988
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #57740539 ← → #57740549

Radix Representation

Decimal 57740540
Binary 11011100010000110011111100 (26 bits)
Octal 0o334206374
Hexadecimal 0x3710CFC

Divisor Catalog (60 of 72)

1 2 4 5 10 11 13 20 22 26 44 52 55 65 110 130 143 169 220 260 286 338 572 676 715 845 1,430 1,553 1,690 1,859 2,860 3,106 3,380 3,718 6,212 7,436 7,765 9,295 15,530 17,083 18,590 20,189 31,060 34,166 37,180 40,378 68,332 80,756 85,415 100,945 170,830 201,890 222,079 262,457 341,660 403,780 444,158 524,914 888,316 1,049,828

Collatz Trajectory (269 steps to reach 1)

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

57,740,540 28,870,270 14,435,135 43,305,406 21,652,703 64,958,110 32,479,055 97,437,166 48,718,583 146,155,750 73,077,875 219,233,626 109,616,813 328,850,440 164,425,220 82,212,610 41,106,305 123,318,916 61,659,458 30,829,729 92,489,188 46,244,594 23,122,297 69,366,892 34,683,446 17,341,723 52,025,170 26,012,585 78,037,756 39,018,878 19,509,439 58,528,318 29,264,159 87,792,478 43,896,239 131,688,718 65,844,359 197,533,078 98,766,539 296,299,618 148,149,809 444,449,428 222,224,714 111,112,357 333,337,072 166,668,536 83,334,268 41,667,134 20,833,567 62,500,702 31,250,351 93,751,054 46,875,527 140,626,582 70,313,291 210,939,874 105,469,937 316,409,812 158,204,906 79,102,453

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