λ
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Atlas › Integer Profiles › Node 36,960,822

36,960,822

2 × 32 × 17 × 43 × 532
Abundant Even Composite

36,960,822 factors as 2 × 3^2 × 17 × 43 × 53^2. Its 72 positive divisors give a proper-divisor sum of 51,471,522, so this integer is abundant. The Collatz stopping time is 333 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 17 × 43 × 53^2
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 88,432,344
Proper Divisor Sum 51,471,522
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #36960811 ← → #36960823

Radix Representation

Decimal 36960822
Binary 10001100111111101000110110 (26 bits)
Octal 0o214775066
Hexadecimal 0x233FA36

Divisor Catalog (60 of 72)

1 2 3 6 9 17 18 34 43 51 53 86 102 106 129 153 159 258 306 318 387 477 731 774 901 954 1,462 1,802 2,193 2,279 2,703 2,809 4,386 4,558 5,406 5,618 6,579 6,837 8,109 8,427 13,158 13,674 16,218 16,854 20,511 25,281 38,743 41,022 47,753 50,562 77,486 95,506 116,229 120,787 143,259 232,458 241,574 286,518 348,687 362,361

Collatz Trajectory (333 steps to reach 1)

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

36,960,822 18,480,411 55,441,234 27,720,617 83,161,852 41,580,926 20,790,463 62,371,390 31,185,695 93,557,086 46,778,543 140,335,630 70,167,815 210,503,446 105,251,723 315,755,170 157,877,585 473,632,756 236,816,378 118,408,189 355,224,568 177,612,284 88,806,142 44,403,071 133,209,214 66,604,607 199,813,822 99,906,911 299,720,734 149,860,367 449,581,102 224,790,551 674,371,654 337,185,827 1,011,557,482 505,778,741 1,517,336,224 758,668,112 379,334,056 189,667,028 94,833,514 47,416,757 142,250,272 71,125,136 35,562,568 17,781,284 8,890,642 4,445,321 13,335,964 6,667,982 3,333,991 10,001,974 5,000,987 15,002,962 7,501,481 22,504,444 11,252,222 5,626,111 16,878,334 8,439,167

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