λ
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Atlas › Integer Profiles › Node 45,618,846

45,618,846

2 × 3 × 7 × 132 × 6427
Abundant Even Composite

45,618,846 factors as 2 × 3 × 7 × 13^2 × 6427. Its 48 positive divisors give a proper-divisor sum of 67,308,258, so this integer is abundant. The Collatz stopping time is 310 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 13^2 × 6427
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 112,927,104
Proper Divisor Sum 67,308,258
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #45618823 ← → #45618863

Radix Representation

Decimal 45618846
Binary 10101110000001011010011110 (26 bits)
Octal 0o256013236
Hexadecimal 0x2B8169E

Divisor Catalog (48)

1 2 3 6 7 13 14 21 26 39 42 78 91 169 182 273 338 507 546 1,014 1,183 2,366 3,549 6,427 7,098 12,854 19,281 38,562 44,989 83,551 89,978 134,967 167,102 250,653 269,934 501,306 584,857 1,086,163 1,169,714 1,754,571 2,172,326 3,258,489 3,509,142 6,516,978 7,603,141 15,206,282 22,809,423 45,618,846

Collatz Trajectory (310 steps to reach 1)

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

45,618,846 22,809,423 68,428,270 34,214,135 102,642,406 51,321,203 153,963,610 76,981,805 230,945,416 115,472,708 57,736,354 28,868,177 86,604,532 43,302,266 21,651,133 64,953,400 32,476,700 16,238,350 8,119,175 24,357,526 12,178,763 36,536,290 18,268,145 54,804,436 27,402,218 13,701,109 41,103,328 20,551,664 10,275,832 5,137,916 2,568,958 1,284,479 3,853,438 1,926,719 5,780,158 2,890,079 8,670,238 4,335,119 13,005,358 6,502,679 19,508,038 9,754,019 29,262,058 14,631,029 43,893,088 21,946,544 10,973,272 5,486,636 2,743,318 1,371,659 4,114,978 2,057,489 6,172,468 3,086,234 1,543,117 4,629,352 2,314,676 1,157,338 578,669 1,736,008

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