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Atlas › Integer Profiles › Node 13,634,840

13,634,840

23 × 5 × 71 × 4801
Abundant Even Composite

13,634,840 factors as 2^3 × 5 × 71 × 4801. Its 32 positive divisors give a proper-divisor sum of 17,482,120, so this integer is abundant. The Collatz stopping time is 223 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 71 × 4801
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 31,116,960
Proper Divisor Sum 17,482,120
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #13634813 ← → #13634851

Radix Representation

Decimal 13634840
Binary 110100000000110100011000 (24 bits)
Octal 0o64006430
Hexadecimal 0xD00D18

Divisor Catalog (32)

1 2 4 5 8 10 20 40 71 142 284 355 568 710 1,420 2,840 4,801 9,602 19,204 24,005 38,408 48,010 96,020 192,040 340,871 681,742 1,363,484 1,704,355 2,726,968 3,408,710 6,817,420 13,634,840

Collatz Trajectory (223 steps to reach 1)

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

13,634,840 6,817,420 3,408,710 1,704,355 5,113,066 2,556,533 7,669,600 3,834,800 1,917,400 958,700 479,350 239,675 719,026 359,513 1,078,540 539,270 269,635 808,906 404,453 1,213,360 606,680 303,340 151,670 75,835 227,506 113,753 341,260 170,630 85,315 255,946 127,973 383,920 191,960 95,980 47,990 23,995 71,986 35,993 107,980 53,990 26,995 80,986 40,493 121,480 60,740 30,370 15,185 45,556 22,778 11,389 34,168 17,084 8,542 4,271 12,814 6,407 19,222 9,611 28,834 14,417

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