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Atlas › Integer Profiles › Node 2,913,664

2,913,664

27 × 13 × 17 × 103
Abundant Even Composite

2,913,664 factors as 2^7 × 13 × 17 × 103. Its 64 positive divisors give a proper-divisor sum of 3,769,376, so this integer is abundant. The Collatz stopping time is 213 steps.

Prime Factor Structure

Factorization String 2^7 × 13 × 17 × 103
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 6,683,040
Proper Divisor Sum 3,769,376
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #2913641 ← → #2913697

Radix Representation

Decimal 2913664
Binary 1011000111010110000000 (22 bits)
Octal 0o13072600
Hexadecimal 0x2C7580

Divisor Catalog (60 of 64)

1 2 4 8 13 16 17 26 32 34 52 64 68 103 104 128 136 206 208 221 272 412 416 442 544 824 832 884 1,088 1,339 1,648 1,664 1,751 1,768 2,176 2,678 3,296 3,502 3,536 5,356 6,592 7,004 7,072 10,712 13,184 14,008 14,144 21,424 22,763 28,016 28,288 42,848 45,526 56,032 85,696 91,052 112,064 171,392 182,104 224,128

Collatz Trajectory (213 steps to reach 1)

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

2,913,664 1,456,832 728,416 364,208 182,104 91,052 45,526 22,763 68,290 34,145 102,436 51,218 25,609 76,828 38,414 19,207 57,622 28,811 86,434 43,217 129,652 64,826 32,413 97,240 48,620 24,310 12,155 36,466 18,233 54,700 27,350 13,675 41,026 20,513 61,540 30,770 15,385 46,156 23,078 11,539 34,618 17,309 51,928 25,964 12,982 6,491 19,474 9,737 29,212 14,606 7,303 21,910 10,955 32,866 16,433 49,300 24,650 12,325 36,976 18,488

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