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Atlas › Integer Profiles › Node 13,776,140

13,776,140

22 × 5 × 7 × 19 × 5179
Abundant Even Composite

13,776,140 factors as 2^2 × 5 × 7 × 19 × 5179. Its 48 positive divisors give a proper-divisor sum of 21,033,460, so this integer is abundant. The Collatz stopping time is 223 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 19 × 5179
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 34,809,600
Proper Divisor Sum 21,033,460
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #13776067 ← → #13776167

Radix Representation

Decimal 13776140
Binary 110100100011010100001100 (24 bits)
Octal 0o64432414
Hexadecimal 0xD2350C

Divisor Catalog (48)

1 2 4 5 7 10 14 19 20 28 35 38 70 76 95 133 140 190 266 380 532 665 1,330 2,660 5,179 10,358 20,716 25,895 36,253 51,790 72,506 98,401 103,580 145,012 181,265 196,802 362,530 393,604 492,005 688,807 725,060 984,010 1,377,614 1,968,020 2,755,228 3,444,035 6,888,070 13,776,140

Collatz Trajectory (223 steps to reach 1)

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

13,776,140 6,888,070 3,444,035 10,332,106 5,166,053 15,498,160 7,749,080 3,874,540 1,937,270 968,635 2,905,906 1,452,953 4,358,860 2,179,430 1,089,715 3,269,146 1,634,573 4,903,720 2,451,860 1,225,930 612,965 1,838,896 919,448 459,724 229,862 114,931 344,794 172,397 517,192 258,596 129,298 64,649 193,948 96,974 48,487 145,462 72,731 218,194 109,097 327,292 163,646 81,823 245,470 122,735 368,206 184,103 552,310 276,155 828,466 414,233 1,242,700 621,350 310,675 932,026 466,013 1,398,040 699,020 349,510 174,755 524,266

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