8,129,576

2³ × 7 × 13² × 859

8,129,576 factors as 2^3 × 7 × 13^2 × 859. Its 48 positive divisors give a proper-divisor sum of 10,756,024, so this integer is abundant. The Collatz stopping time is 261 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 13^2 × 859

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 18,885,600

Proper Divisor Sum 10,756,024

Digit Sum / Digital Root 38 (Root: 2)

Adjacent Primes #8129567 ← → #8129629

Radix Representation

Decimal	8129576
Binary	11111000000110000101000 (23 bits)
Octal	0o37006050
Hexadecimal	0x7C0C28

Divisor Catalog (48)

1 2 4 7 8 13 14 26 28 52 56 91 104 169 182 338 364 676 728 859 1,183 1,352 1,718 2,366 3,436 4,732 6,013 6,872 9,464 11,167 12,026 22,334 24,052 44,668 48,104 78,169 89,336 145,171 156,338 290,342 312,676 580,684 625,352 1,016,197 1,161,368 2,032,394 4,064,788 8,129,576

Collatz Trajectory (261 steps to reach 1)

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

8,129,576 4,064,788 2,032,394 1,016,197 3,048,592 1,524,296 762,148 381,074 190,537 571,612 285,806 142,903 428,710 214,355 643,066 321,533 964,600 482,300 241,150 120,575 361,726 180,863 542,590 271,295 813,886 406,943 1,220,830 610,415 1,831,246 915,623 2,746,870 1,373,435 4,120,306 2,060,153 6,180,460 3,090,230 1,545,115 4,635,346 2,317,673 6,953,020 3,476,510 1,738,255 5,214,766 2,607,383 7,822,150 3,911,075 11,733,226 5,866,613 17,599,840 8,799,920 4,399,960 2,199,980 1,099,990 549,995 1,649,986 824,993 2,474,980 1,237,490 618,745 1,856,236

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