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Atlas › Integer Profiles › Node 13,000,000

13,000,000

26 × 56 × 13
Abundant Even Composite

13,000,000 factors as 2^6 × 5^6 × 13. Its 98 positive divisors give a proper-divisor sum of 21,726,118, so this integer is abundant. The Collatz stopping time is 47 steps.

Prime Factor Structure

Factorization String 2^6 × 5^6 × 13
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 98
Divisor Sum (σ) 34,726,118
Proper Divisor Sum 21,726,118
Digit Sum / Digital Root 4 (Root: 4)
Adjacent Primes #12999997 ← → #13000027

Radix Representation

Decimal 13000000
Binary 110001100101110101000000 (24 bits)
Octal 0o61456500
Hexadecimal 0xC65D40

Divisor Catalog (60 of 98)

1 2 4 5 8 10 13 16 20 25 26 32 40 50 52 64 65 80 100 104 125 130 160 200 208 250 260 320 325 400 416 500 520 625 650 800 832 1,000 1,040 1,250 1,300 1,600 1,625 2,000 2,080 2,500 2,600 3,125 3,250 4,000 4,160 5,000 5,200 6,250 6,500 8,000 8,125 10,000 10,400 12,500

Collatz Trajectory (47 steps to reach 1)

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

13,000,000 6,500,000 3,250,000 1,625,000 812,500 406,250 203,125 609,376 304,688 152,344 76,172 38,086 19,043 57,130 28,565 85,696 42,848 21,424 10,712 5,356 2,678 1,339 4,018 2,009 6,028 3,014 1,507 4,522 2,261 6,784 3,392 1,696 848 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1

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