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Atlas › Integer Profiles › Node 7,680,465

7,680,465

32 × 5 × 13 × 19 × 691
Deficient Odd Composite

7,680,465 factors as 3^2 × 5 × 13 × 19 × 691. Its 48 positive divisors give a proper-divisor sum of 7,432,815, so this integer is deficient. The Collatz stopping time is 72 steps.

Prime Factor Structure

Factorization String 3^2 × 5 × 13 × 19 × 691
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 15,113,280
Proper Divisor Sum 7,432,815
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #7680437 ← → #7680469

Radix Representation

Decimal 7680465
Binary 11101010011000111010001 (23 bits)
Octal 0o35230721
Hexadecimal 0x7531D1

Divisor Catalog (48)

1 3 5 9 13 15 19 39 45 57 65 95 117 171 195 247 285 585 691 741 855 1,235 2,073 2,223 3,455 3,705 6,219 8,983 10,365 11,115 13,129 26,949 31,095 39,387 44,915 65,645 80,847 118,161 134,745 170,677 196,935 404,235 512,031 590,805 853,385 1,536,093 2,560,155 7,680,465

Collatz Trajectory (72 steps to reach 1)

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

7,680,465 23,041,396 11,520,698 5,760,349 17,281,048 8,640,524 4,320,262 2,160,131 6,480,394 3,240,197 9,720,592 4,860,296 2,430,148 1,215,074 607,537 1,822,612 911,306 455,653 1,366,960 683,480 341,740 170,870 85,435 256,306 128,153 384,460 192,230 96,115 288,346 144,173 432,520 216,260 108,130 54,065 162,196 81,098 40,549 121,648 60,824 30,412 15,206 7,603 22,810 11,405 34,216 17,108 8,554 4,277 12,832 6,416 3,208 1,604 802 401 1,204 602 301 904 452 226

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