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Atlas › Integer Profiles › Node 33,905,410

33,905,410

2 × 5 × 7 × 112 × 4003
Abundant Even Composite

33,905,410 factors as 2 × 5 × 7 × 11^2 × 4003. Its 48 positive divisors give a proper-divisor sum of 42,779,198, so this integer is abundant. The Collatz stopping time is 108 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 11^2 × 4003
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 76,684,608
Proper Divisor Sum 42,779,198
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #33905407 ← → #33905419

Radix Representation

Decimal 33905410
Binary 10000001010101101100000010 (26 bits)
Octal 0o201255402
Hexadecimal 0x2055B02

Divisor Catalog (48)

1 2 5 7 10 11 14 22 35 55 70 77 110 121 154 242 385 605 770 847 1,210 1,694 4,003 4,235 8,006 8,470 20,015 28,021 40,030 44,033 56,042 88,066 140,105 220,165 280,210 308,231 440,330 484,363 616,462 968,726 1,541,155 2,421,815 3,082,310 3,390,541 4,843,630 6,781,082 16,952,705 33,905,410

Collatz Trajectory (108 steps to reach 1)

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

33,905,410 16,952,705 50,858,116 25,429,058 12,714,529 38,143,588 19,071,794 9,535,897 28,607,692 14,303,846 7,151,923 21,455,770 10,727,885 32,183,656 16,091,828 8,045,914 4,022,957 12,068,872 6,034,436 3,017,218 1,508,609 4,525,828 2,262,914 1,131,457 3,394,372 1,697,186 848,593 2,545,780 1,272,890 636,445 1,909,336 954,668 477,334 238,667 716,002 358,001 1,074,004 537,002 268,501 805,504 402,752 201,376 100,688 50,344 25,172 12,586 6,293 18,880 9,440 4,720 2,360 1,180 590 295 886 443 1,330 665 1,996 998

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