λ
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Atlas › Integer Profiles › Node 65,193,772

65,193,772

22 × 7 × 41 × 109 × 521
Abundant Even Composite

65,193,772 factors as 2^2 × 7 × 41 × 109 × 521. Its 48 positive divisors give a proper-divisor sum of 69,858,068, so this integer is abundant. The Collatz stopping time is 114 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 41 × 109 × 521
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 135,051,840
Proper Divisor Sum 69,858,068
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #65193767 ← → #65193787

Radix Representation

Decimal 65193772
Binary 11111000101100011100101100 (26 bits)
Octal 0o370543454
Hexadecimal 0x3E2C72C

Divisor Catalog (48)

1 2 4 7 14 28 41 82 109 164 218 287 436 521 574 763 1,042 1,148 1,526 2,084 3,052 3,647 4,469 7,294 8,938 14,588 17,876 21,361 31,283 42,722 56,789 62,566 85,444 113,578 125,132 149,527 227,156 299,054 397,523 598,108 795,046 1,590,092 2,328,349 4,656,698 9,313,396 16,298,443 32,596,886 65,193,772

Collatz Trajectory (114 steps to reach 1)

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

65,193,772 32,596,886 16,298,443 48,895,330 24,447,665 73,342,996 36,671,498 18,335,749 55,007,248 27,503,624 13,751,812 6,875,906 3,437,953 10,313,860 5,156,930 2,578,465 7,735,396 3,867,698 1,933,849 5,801,548 2,900,774 1,450,387 4,351,162 2,175,581 6,526,744 3,263,372 1,631,686 815,843 2,447,530 1,223,765 3,671,296 1,835,648 917,824 458,912 229,456 114,728 57,364 28,682 14,341 43,024 21,512 10,756 5,378 2,689 8,068 4,034 2,017 6,052 3,026 1,513 4,540 2,270 1,135 3,406 1,703 5,110 2,555 7,666 3,833 11,500

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