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Atlas › Integer Profiles › Node 72,048,618

72,048,618

2 × 32 × 17 × 173 × 1361
Abundant Even Composite

72,048,618 factors as 2 × 3^2 × 17 × 173 × 1361. Its 48 positive divisors give a proper-divisor sum of 94,316,958, so this integer is abundant. The Collatz stopping time is 202 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 17 × 173 × 1361
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 166,365,576
Proper Divisor Sum 94,316,958
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #72048611 ← → #72048623

Radix Representation

Decimal 72048618
Binary 100010010110101111111101010 (27 bits)
Octal 0o422657752
Hexadecimal 0x44B5FEA

Divisor Catalog (48)

1 2 3 6 9 17 18 34 51 102 153 173 306 346 519 1,038 1,361 1,557 2,722 2,941 3,114 4,083 5,882 8,166 8,823 12,249 17,646 23,137 24,498 26,469 46,274 52,938 69,411 138,822 208,233 235,453 416,466 470,906 706,359 1,412,718 2,119,077 4,002,701 4,238,154 8,005,402 12,008,103 24,016,206 36,024,309 72,048,618

Collatz Trajectory (202 steps to reach 1)

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

72,048,618 36,024,309 108,072,928 54,036,464 27,018,232 13,509,116 6,754,558 3,377,279 10,131,838 5,065,919 15,197,758 7,598,879 22,796,638 11,398,319 34,194,958 17,097,479 51,292,438 25,646,219 76,938,658 38,469,329 115,407,988 57,703,994 28,851,997 86,555,992 43,277,996 21,638,998 10,819,499 32,458,498 16,229,249 48,687,748 24,343,874 12,171,937 36,515,812 18,257,906 9,128,953 27,386,860 13,693,430 6,846,715 20,540,146 10,270,073 30,810,220 15,405,110 7,702,555 23,107,666 11,553,833 34,661,500 17,330,750 8,665,375 25,996,126 12,998,063 38,994,190 19,497,095 58,491,286 29,245,643 87,736,930 43,868,465 131,605,396 65,802,698 32,901,349 98,704,048

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