λ
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Atlas › Integer Profiles › Node 73,071,908

73,071,908

22 × 7 × 13 × 103 × 1949
Abundant Even Composite

73,071,908 factors as 2^2 × 7 × 13 × 103 × 1949. Its 48 positive divisors give a proper-divisor sum of 85,923,292, so this integer is abundant. The Collatz stopping time is 197 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 13 × 103 × 1949
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 158,995,200
Proper Divisor Sum 85,923,292
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #73071871 ← → #73071953

Radix Representation

Decimal 73071908
Binary 100010110101111110100100100 (27 bits)
Octal 0o426576444
Hexadecimal 0x45AFD24

Divisor Catalog (48)

1 2 4 7 13 14 26 28 52 91 103 182 206 364 412 721 1,339 1,442 1,949 2,678 2,884 3,898 5,356 7,796 9,373 13,643 18,746 25,337 27,286 37,492 50,674 54,572 101,348 177,359 200,747 354,718 401,494 709,436 802,988 1,405,229 2,609,711 2,810,458 5,219,422 5,620,916 10,438,844 18,267,977 36,535,954 73,071,908

Collatz Trajectory (197 steps to reach 1)

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

73,071,908 36,535,954 18,267,977 54,803,932 27,401,966 13,700,983 41,102,950 20,551,475 61,654,426 30,827,213 92,481,640 46,240,820 23,120,410 11,560,205 34,680,616 17,340,308 8,670,154 4,335,077 13,005,232 6,502,616 3,251,308 1,625,654 812,827 2,438,482 1,219,241 3,657,724 1,828,862 914,431 2,743,294 1,371,647 4,114,942 2,057,471 6,172,414 3,086,207 9,258,622 4,629,311 13,887,934 6,943,967 20,831,902 10,415,951 31,247,854 15,623,927 46,871,782 23,435,891 70,307,674 35,153,837 105,461,512 52,730,756 26,365,378 13,182,689 39,548,068 19,774,034 9,887,017 29,661,052 14,830,526 7,415,263 22,245,790 11,122,895 33,368,686 16,684,343

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