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Atlas › Integer Profiles › Node 73,065,076

73,065,076

22 × 72 × 163 × 2287
Abundant Even Composite

73,065,076 factors as 2^2 × 7^2 × 163 × 2287. Its 36 positive divisors give a proper-divisor sum of 76,652,492, so this integer is abundant. The Collatz stopping time is 228 steps.

Prime Factor Structure

Factorization String 2^2 × 7^2 × 163 × 2287
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 149,717,568
Proper Divisor Sum 76,652,492
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #73065059 ← → #73065101

Radix Representation

Decimal 73065076
Binary 100010110101110001001110100 (27 bits)
Octal 0o426561164
Hexadecimal 0x45AE274

Divisor Catalog (36)

1 2 4 7 14 28 49 98 163 196 326 652 1,141 2,282 2,287 4,564 4,574 7,987 9,148 15,974 16,009 31,948 32,018 64,036 112,063 224,126 372,781 448,252 745,562 1,491,124 2,609,467 5,218,934 10,437,868 18,266,269 36,532,538 73,065,076

Collatz Trajectory (228 steps to reach 1)

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

73,065,076 36,532,538 18,266,269 54,798,808 27,399,404 13,699,702 6,849,851 20,549,554 10,274,777 30,824,332 15,412,166 7,706,083 23,118,250 11,559,125 34,677,376 17,338,688 8,669,344 4,334,672 2,167,336 1,083,668 541,834 270,917 812,752 406,376 203,188 101,594 50,797 152,392 76,196 38,098 19,049 57,148 28,574 14,287 42,862 21,431 64,294 32,147 96,442 48,221 144,664 72,332 36,166 18,083 54,250 27,125 81,376 40,688 20,344 10,172 5,086 2,543 7,630 3,815 11,446 5,723 17,170 8,585 25,756 12,878

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