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Atlas › Integer Profiles › Node 7,680,205

7,680,205

5 × 132 × 61 × 149
Deficient Odd Composite

7,680,205 factors as 5 × 13^2 × 61 × 149. Its 24 positive divisors give a proper-divisor sum of 2,531,195, so this integer is deficient. The Collatz stopping time is 124 steps.

Prime Factor Structure

Factorization String 5 × 13^2 × 61 × 149
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 10,211,400
Proper Divisor Sum 2,531,195
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #7680191 ← → #7680217

Radix Representation

Decimal 7680205
Binary 11101010011000011001101 (23 bits)
Octal 0o35230315
Hexadecimal 0x7530CD

Divisor Catalog (24)

1 5 13 61 65 149 169 305 745 793 845 1,937 3,965 9,089 9,685 10,309 25,181 45,445 51,545 118,157 125,905 590,785 1,536,041 7,680,205

Collatz Trajectory (124 steps to reach 1)

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

7,680,205 23,040,616 11,520,308 5,760,154 2,880,077 8,640,232 4,320,116 2,160,058 1,080,029 3,240,088 1,620,044 810,022 405,011 1,215,034 607,517 1,822,552 911,276 455,638 227,819 683,458 341,729 1,025,188 512,594 256,297 768,892 384,446 192,223 576,670 288,335 865,006 432,503 1,297,510 648,755 1,946,266 973,133 2,919,400 1,459,700 729,850 364,925 1,094,776 547,388 273,694 136,847 410,542 205,271 615,814 307,907 923,722 461,861 1,385,584 692,792 346,396 173,198 86,599 259,798 129,899 389,698 194,849 584,548 292,274

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