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Atlas › Integer Profiles › Node 37,101,306

37,101,306

2 × 3 × 11 × 37 × 15193
Abundant Even Composite

37,101,306 factors as 2 × 3 × 11 × 37 × 15193. Its 32 positive divisors give a proper-divisor sum of 46,040,262, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2 × 3 × 11 × 37 × 15193
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 83,141,568
Proper Divisor Sum 46,040,262
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #37101271 ← → #37101307

Radix Representation

Decimal 37101306
Binary 10001101100001111011111010 (26 bits)
Octal 0o215417372
Hexadecimal 0x2361EFA

Divisor Catalog (32)

1 2 3 6 11 22 33 37 66 74 111 222 407 814 1,221 2,442 15,193 30,386 45,579 91,158 167,123 334,246 501,369 562,141 1,002,738 1,124,282 1,686,423 3,372,846 6,183,551 12,367,102 18,550,653 37,101,306

Collatz Trajectory (165 steps to reach 1)

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

37,101,306 18,550,653 55,651,960 27,825,980 13,912,990 6,956,495 20,869,486 10,434,743 31,304,230 15,652,115 46,956,346 23,478,173 70,434,520 35,217,260 17,608,630 8,804,315 26,412,946 13,206,473 39,619,420 19,809,710 9,904,855 29,714,566 14,857,283 44,571,850 22,285,925 66,857,776 33,428,888 16,714,444 8,357,222 4,178,611 12,535,834 6,267,917 18,803,752 9,401,876 4,700,938 2,350,469 7,051,408 3,525,704 1,762,852 881,426 440,713 1,322,140 661,070 330,535 991,606 495,803 1,487,410 743,705 2,231,116 1,115,558 557,779 1,673,338 836,669 2,510,008 1,255,004 627,502 313,751 941,254 470,627 1,411,882

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