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Atlas › Integer Profiles › Node 2,829,138

2,829,138

2 × 3 × 13 × 19 × 23 × 83
Abundant Even Composite

2,829,138 factors as 2 × 3 × 13 × 19 × 23 × 83. Its 64 positive divisors give a proper-divisor sum of 3,944,622, so this integer is abundant. The Collatz stopping time is 107 steps.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 19 × 23 × 83
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 6,773,760
Proper Divisor Sum 3,944,622
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #2829133 ← → #2829139

Radix Representation

Decimal 2829138
Binary 1010110010101101010010 (22 bits)
Octal 0o12625522
Hexadecimal 0x2B2B52

Divisor Catalog (60 of 64)

1 2 3 6 13 19 23 26 38 39 46 57 69 78 83 114 138 166 247 249 299 437 494 498 598 741 874 897 1,079 1,311 1,482 1,577 1,794 1,909 2,158 2,622 3,154 3,237 3,818 4,731 5,681 5,727 6,474 9,462 11,362 11,454 17,043 20,501 24,817 34,086 36,271 41,002 49,634 61,503 72,542 74,451 108,813 123,006 148,902 217,626

Collatz Trajectory (107 steps to reach 1)

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

2,829,138 1,414,569 4,243,708 2,121,854 1,060,927 3,182,782 1,591,391 4,774,174 2,387,087 7,161,262 3,580,631 10,741,894 5,370,947 16,112,842 8,056,421 24,169,264 12,084,632 6,042,316 3,021,158 1,510,579 4,531,738 2,265,869 6,797,608 3,398,804 1,699,402 849,701 2,549,104 1,274,552 637,276 318,638 159,319 477,958 238,979 716,938 358,469 1,075,408 537,704 268,852 134,426 67,213 201,640 100,820 50,410 25,205 75,616 37,808 18,904 9,452 4,726 2,363 7,090 3,545 10,636 5,318 2,659 7,978 3,989 11,968 5,984 2,992

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