λ
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Atlas › Integer Profiles › Node 21,515,390

21,515,390

2 × 5 × 132 × 29 × 439
Abundant Even Composite

21,515,390 factors as 2 × 5 × 13^2 × 29 × 439. Its 48 positive divisors give a proper-divisor sum of 21,965,410, so this integer is abundant. The Collatz stopping time is 172 steps.

Prime Factor Structure

Factorization String 2 × 5 × 13^2 × 29 × 439
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 43,480,800
Proper Divisor Sum 21,965,410
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #21515381 ← → #21515411

Radix Representation

Decimal 21515390
Binary 1010010000100110001111110 (25 bits)
Octal 0o122046176
Hexadecimal 0x1484C7E

Divisor Catalog (48)

1 2 5 10 13 26 29 58 65 130 145 169 290 338 377 439 754 845 878 1,690 1,885 2,195 3,770 4,390 4,901 5,707 9,802 11,414 12,731 24,505 25,462 28,535 49,010 57,070 63,655 74,191 127,310 148,382 165,503 331,006 370,955 741,910 827,515 1,655,030 2,151,539 4,303,078 10,757,695 21,515,390

Collatz Trajectory (172 steps to reach 1)

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

21,515,390 10,757,695 32,273,086 16,136,543 48,409,630 24,204,815 72,614,446 36,307,223 108,921,670 54,460,835 163,382,506 81,691,253 245,073,760 122,536,880 61,268,440 30,634,220 15,317,110 7,658,555 22,975,666 11,487,833 34,463,500 17,231,750 8,615,875 25,847,626 12,923,813 38,771,440 19,385,720 9,692,860 4,846,430 2,423,215 7,269,646 3,634,823 10,904,470 5,452,235 16,356,706 8,178,353 24,535,060 12,267,530 6,133,765 18,401,296 9,200,648 4,600,324 2,300,162 1,150,081 3,450,244 1,725,122 862,561 2,587,684 1,293,842 646,921 1,940,764 970,382 485,191 1,455,574 727,787 2,183,362 1,091,681 3,275,044 1,637,522 818,761

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