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Atlas › Integer Profiles › Node 65,716,644

65,716,644

22 × 3 × 72 × 73 × 1531
Abundant Even Composite

65,716,644 factors as 2^2 × 3 × 7^2 × 73 × 1531. Its 72 positive divisors give a proper-divisor sum of 115,218,684, so this integer is abundant. The Collatz stopping time is 171 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7^2 × 73 × 1531
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 180,935,328
Proper Divisor Sum 115,218,684
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #65716643 ← → #65716657

Radix Representation

Decimal 65716644
Binary 11111010101100000110100100 (26 bits)
Octal 0o372540644
Hexadecimal 0x3EAC1A4

Divisor Catalog (60 of 72)

1 2 3 4 6 7 12 14 21 28 42 49 73 84 98 146 147 196 219 292 294 438 511 588 876 1,022 1,531 1,533 2,044 3,062 3,066 3,577 4,593 6,124 6,132 7,154 9,186 10,717 10,731 14,308 18,372 21,434 21,462 32,151 42,868 42,924 64,302 75,019 111,763 128,604 150,038 223,526 225,057 300,076 335,289 447,052 450,114 670,578 782,341 900,228

Collatz Trajectory (171 steps to reach 1)

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

65,716,644 32,858,322 16,429,161 49,287,484 24,643,742 12,321,871 36,965,614 18,482,807 55,448,422 27,724,211 83,172,634 41,586,317 124,758,952 62,379,476 31,189,738 15,594,869 46,784,608 23,392,304 11,696,152 5,848,076 2,924,038 1,462,019 4,386,058 2,193,029 6,579,088 3,289,544 1,644,772 822,386 411,193 1,233,580 616,790 308,395 925,186 462,593 1,387,780 693,890 346,945 1,040,836 520,418 260,209 780,628 390,314 195,157 585,472 292,736 146,368 73,184 36,592 18,296 9,148 4,574 2,287 6,862 3,431 10,294 5,147 15,442 7,721 23,164 11,582

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